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Rates, SM-Bank 103

 Each stage of Moira's 30 km charity fitness challenge is outlined below.

  • Moira started the challenge with a running leg and ran 10 kilometres in 1.5 hours.
  • She then stopped for 30 minutes.
  • Her next leg involved cycling and she averaged 40 km/h for the next half an hour.
  • Moira then stopped and had lunch for 1.5 hours.
  • She walked with her friends for the next hour averaging 5 km/h.
  • Moira stopped for half an hour for afternoon tea and completed the challenge in a total of 7 hours.

Draw a distance-time graph to represent Moira's challenge on the following grid. Include the scale on both axes.  (3 marks)
 

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Show Worked Solution

Rates, SM-Bank 101

Roland left home at 9 a.m. and travelled through the city averaging 60 km/h for 2 hours.

He then stopped for half an hour at a roadhouse.

Roland continued his journey on the motorway and averaged 100 km/h arriving at his destination after 2 hours.
 

Draw a distance-time graph to represent Roland's journey on the following grid, completing times and distances on the axes.  (3 marks)
 

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Show Worked Solution

Rates, SM-Bank 100

The distance-time graph shows the first two stages of a car journey from home to a holiday house.
  

  1. At what speed, in kilometres per hour, did the car travel during stage A of the journey?  (1 mark)

  2. For how long did the car stop during stage B of the journey?  (1 mark)

  3. After stage B, the car continues to travel towards the holiday house at a constant speed of 50 km/h for 2 hours. Graph this part of the journey on the grid above. (2 marks)

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a.    \(100\text{ km/h}\)

b.    \(30\text{ minutes}\)

c.   

Show Worked Solution

a.    \(S=\dfrac{D}{T}\)

\(S=\dfrac{150}{1.5}=100\text{ km/h}\)

b.    \(\text{Stage}\ B=1.5\rightarrow 2\text{ hours}=30\text{ minutes}\)

c.    \(\text{Position at time 4 hours at 50km/h}=150+2\times 50 = 250\ \text{km} \)

Rates, SM-Bank 099

The distance-time graph below shows Clive's walk home from school.

  1. How far did Clive walk in the first minute?  (1 mark)

  2. How far had Clive walked before he stopped to wait for the traffic lights to change to green?  (1 mark)

  3. How far is Clive's home from the school?  (1 mark)

  4. What was Clive's average speed during the first 2 minutes?  (2 marks)

  5. What was Clive's average speed for the entire trip?  (2 marks)

  6. During which times is the graph the steepest? What can you say about Clive's speed in this section? (2 marks)

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a.    \(40\ \text{m}\)

b.    \(240\ \text{m}\)

c.    \(320\ \text{m}\)

d.    \(40\ \text{m/minute}\)

e.    \(64\ \text{m/minute}\)

f.    \(\text{The graph was steepest between the 2nd and 3rd minutes.}\)

\(\text{This is where Clive was walking the fastest.}\)

Show Worked Solution

a.    \(40\ \text{m}\)

b.    \(240\ \text{m}\)

c.    \(320\ \text{m}\)

d.    
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
    \(=\dfrac{80}{2}\)
    \(=40\ \text{m/minute}\)

 

e.    
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
    \(=\dfrac{320}{5}\)
    \(=64\ \text{m/minute}\)

 
f.    \(\text{The graph was steepest between the 2nd and 3rd minutes.}\)

\(\text{This is where Clive was walking the fastest.}\)

Rates, SM-Bank 098

The distance-time graph below shows Betty's train trip to her Grandmother's house in the Blue Mountains and the return journey in her Grandmother's car.

  1. Which section of the the graph shows where Betty had to change trains and wait to catch the next train?  (1 mark)

  2. How long did Betty take to complete section C?  (1 mark)

  3. After how many hours did Betty reach her Grandmother's house?  (1 mark)

  4. What was Betty's average speed for section D?  (2 marks)

  5. How many kilometres did Betty travel in total?  ( 2 marks)

  6. What was Betty's average speed for the entire trip?  (2 marks)

  7. Which section of the graph is the steepest? What can you say about Betty's speed in this section? (2 marks)

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a.    \(\textit{B}\)

b.    \(1 \text{ hour}\)

c.    \(2.5 \text{ hours}\)

d.    \(80\ \text{km/h}\)

e.    \(240\ \text{km}\)

f.     \(60\ \text{km/h}\)

g.    \(\text{The graph was steepest in Section }\textit{A}.\)

\(\text{This is where Betty was travelling the fastest.}\)

Show Worked Solution

a.    \(\text{Horizontal sections of the graph indicate the person}\)

\(\text{is not moving.}\)

\(\therefore\ \text{Betty waited for the next train in section}\ \textit{B}.\)

b.    \(1 \text{ hour}\)

c.    \(2.5 \text{ hours}\)

d.    
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
    \(=\dfrac{120}{1.5}\)
    \(=80\ \text{km/h}\)

 
e.    \(\text{Total distance}=2\times 120=240\ \text{km}\)

f.    
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
    \(=\dfrac{240}{4}\)
    \(=60\ \text{km/h}\)

 
g.    \(\text{The graph was steepest in Section }\textit{A}.\)

\(\text{This is where Betty was travelling the fastest.}\)

Rates, SM-Bank 097

Caleb is travelling from Brisbane to Toowoomba. The journey is 135 kilometres.

His car uses 9.45 litres of fuel per 100 kilometres.

How much fuel will Caleb need to make the journey?

Round your answer to the nearest litre.  (2 marks)

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\(13\ \text{litres  (nearest whole)}\)

Show Worked Solution
\(\text{Fuel needed}\) \(=\dfrac{135}{100}\times 9.45\)
  \(= 12.75\dots\)
  \(= 13\ \text{litres  (nearest whole)}\)

Rates, SM-Bank 096

Mika is making lemonade.

The recipe says she needs 1 cup of sugar for every 3 lemons.

If 7 lemons are used, how many cups of sugar are needed?  (2 marks)

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\(2\dfrac{1}{3}\ \text{cups}\)

Show Worked Solution

\(\text{3 lemons}\rightarrow 1\ \text{cup of sugar}\)

\(\text{1 lemon}\rightarrow\dfrac{1}{3}\ \text{cup of sugar}\)

\(\therefore\ 7\ \text{lemons}\) \(=7\times\dfrac{1}{3}\)
  \(=\dfrac{7}{3}\)
  \(=2\dfrac{1}{3}\ \text{cups}\)

Rates, SM-Bank 095

Johnno and Zoey are driving from Wahroonga to Ballarat which is a distance of 825 kilometres.

After every two hours of driving, they rest for 20 minutes and swap drivers.

How long will their trip take if they average 100 km/h when driving?  (2 marks)

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\(9\ \text{h }35\ \text{min}\)

Show Worked Solution

\(\text{Driving time}=\dfrac{825}{100}=8.25\ \text{h}\)

\(\text{Number of stops}=4\)

\(\therefore\ \text{Total trip time}\) \(=8\ \text{h }15\ \text{m}+(4\times 20)\ \text{m}\)
  \(=8\ \text{h }15\ \text{m}+1\ \text{h }20\ \text{m}\)
  \(=9\ \text{h }35\ \text{min}\)

Rates, SM-Bank 094

Roy and Siegfried are driving from Broken Hill to Albury which is a distance of 840 kilometres.

After every two hours of driving, they rest for 20 minutes and swap drivers.

How long will their trip take if they average 80 km/h when driving?  (2 marks)

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\(12\ \text{h }10\ \text{min}\)

Show Worked Solution

\(\text{Driving time}=\dfrac{840}{80}=10.5\ \text{h}\)

\(\text{Number of stops}=5\)

\(\therefore\ \text{Total trip time}\) \(=10\ \text{h }30\ \text{m}+(5\times 20)\ \text{m}\)
  \(=10\ \text{h }30\ \text{m}+1\ \text{h }40\ \text{m}\)
  \(=12\ \text{h }10\ \text{min}\)

Rates, SM-Bank 093

Oscar and Lucinda are driving from Dungog to Bourke which is a distance of 735 kilometres.

After every two hours of driving, they rest for 15 minutes and swap drivers.

How long will their trip take if they average 70 km/h when driving?  (2 marks)

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\(11\ \text{h }45\ \text{min}\)

Show Worked Solution

\(\text{Driving time}=\dfrac{735}{70}=10.5\ \text{h}\)

\(\text{Number of stops}=5\)

\(\therefore\ \text{Total trip time}\) \(=10\ \text{h }30\ \text{m}+(5\times 15)\ \text{m}\)
  \(=10\ \text{h }30\ \text{m}+1\ \text{h }15\ \text{m}\)
  \(=11\ \text{h }45\ \text{min}\)

Rates, SM-Bank 092 MC

Jenny needs to reduce her discretionary spending which is shown in the table below.
  

Spend Amount How Often
Gym membership $50 Monthly
Air travel $120 Quarterly
KFC lunch $14 2 days per week
Football tickets for 26 rounds $25 Weekly

  

Which action will save her the most?

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\(D\)

Show Worked Solution

\(\text{Calculate the yearly saving of each action}\)

\(\text{Gym membership}=$50\times 12 =$600\)

\(\text{Air travel}=$120\times 4=$480\)

\(\text{KFC lunch}=\bigg(\dfrac{14\times 52}{2}\bigg)=$364\)

\(\text{Football tickets}=26\times 25=$650\)

\(\text{Penrith Panthers tickets costs the most each year}\)
\(\text{so she should stop going to Penrith games.}\)

\(\Rightarrow D\)

Rates, SM-Bank 091 MC

Rhonda needs to reduce her discretionary spending which is shown in the table below.

Spend Amount How Often
Car Wash $80 Monthly
Hairdresser $150 Quarterly
Thai take-away $15 2 nights per week
Streaming services $12 Weekly

Which action will save her the most?

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\(A\)

Show Worked Solution

\(\text{Calculate the yearly saving of each action}\)

\(\text{Car wash}=$80\times 12 =$960\)

\(\text{Hairdresser}=$150\times 4=$600\)

\(\text{Thai}=15\times 52=$780\)

\(\text{Streaming services}=12\times 52=$624\)

\(\text{Washing the car costs the most each year}\)
\(\text{so she should stop washing the car.}\)

\(\Rightarrow A\)

Rates, SM-Bank 090 MC

Choon is travelling at 90 km/h in his car.

If he maintains this speed, how many kilometres will he travel in 20 minutes?

  1. 3
  2. 22.5
  3. 30
  4. 110
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\(C\)

Show Worked Solution
\(\text{Distance}\) \(=\text{speed}\times \text{time}\)
  \(=90\times \dfrac{20}{60}\)
  \(=90\times \dfrac{1}{3}\)
  \(=30\ \text{km}\)

\(\Rightarrow C\)

Rates, SM-Bank 089 MC

The exchange rate between Australian dollars and Euro dollars (€) is A$1 = €0.5.

Leisa is in Paris and buys a baguette that costs €12.

What change, in Euro dollars (€), will Leisa receive from A$50?

  1. €13
  2. €38
  3. €76
  4. €94
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\(A\)

Show Worked Solution

\(\text{Convert A}\$50\ \text{to Euro dollars(€):}\)

\(\text{A}$50\) \(=50\times 0.5\)
  \(=\text{€}25\)

 

\(\text{Change}\) \(=\text{€}25-\text{€}12\)
  \(=\text{€}13\)

\(\Rightarrow A\)

Rates, SM-Bank 088 MC

The exchange rate between Australian dollars and Euro dollars (€) isA$1 = €0.5.

Murray is in Europe and takes a taxi that costs €20.

What change, in Euro dollars (€), will Murray receive from A$50?

  1. €5
  2. €10
  3. €60
  4. €80
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\(A\)

Show Worked Solution

\(\text{Convert A}$50\ \text{to Euro dollars(€):}\)

\(\text{A}$50\) \(=50\times 0.5\)
  \(=\text{€}25\)

 

\(\text{Change}\) \(=\text{€}25-\text{€}20\)
  \(=\text{€}5\)

\(\Rightarrow A\)

Rates, SM-Bank 085 MC

The nutritional information on a breakfast cereal is shown below.

 

 
Kylie expends 1000 kJ of energy by rowing for 30 minutes.

If she consumes 100 grams of the cereal, approximately how long should she row to use up the energy it provides?

  1. 45 minutes
  2. 60 minutes
  3. 65 minutes
  4. 75 minutes
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\(D\)

Show Worked Solution

\(100\ \text{grams of cereal}\rightarrow 2460\ \text{kJ}\)

\(\text{Exercise required}\) \(=\dfrac{2460}{1000}\times 30\)
  \(\approx 2.5\times 30\)
  \(\approx 75\ \text{minutes}\)

 
\(\Rightarrow D\)

Rates, SM-Bank 084 MC

The nutritional information on a power bar is shown below.

 

 
Sandra expends 900 kJ of energy by running for 20 minutes.

If she consumes 100 grams of the power bar, approximately how long should she run to use up the energy it provides?
 

  1. 20 minutes
  2. 30 minutes
  3. 40 minutes
  4. 55 minutes
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\(C\)

Show Worked Solution

\(100\ \text{grams of power bar}\rightarrow 1810\ \text{kJ}\)

\(\text{Exercise required}\) \(=\dfrac{1810}{900}\times 20\)
  \(\approx 2\times 20\)
  \(\approx 40\ \text{minutes}\)

 
\(\Rightarrow C\)

Rates, SM-Bank 083 MC

The nutritional information on a breakfast cereal is shown below.

 

 

Anna expends 650 kJ of energy by swimming for 30 minutes.

If she consumes 100 grams of the cereal, approximately how long should she swim to use up the energy it provides?

  1. 30 minutes
  2. 45 minutes
  3. 60 minutes
  4. 75 minutes
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\(C\)

Show Worked Solution

\(100\ \text{grams of cereal}\rightarrow 1320\ \text{kJ}\)

\(\text{Exercise required}\) \(=\dfrac{1320}{650}\times 30\)
  \(\approx 2\times 30\)
  \(\approx 60\ \text{minutes}\)

 
\(\Rightarrow C\)

Rates, SM-Bank 082 MC

The nutritional information on a breakfast cereal is shown below.

 

 
Marjorie expends 1000 kJ of energy by jogging for 30 minutes.

If she consumes 100 grams of the cereal, approximately how long should she jog to use up the energy it provides?

  1. 30 minutes
  2. 40 minutes
  3. 60 minutes
  4. 80 minutes
Show Answers Only

\(B\)

Show Worked Solution

\(100\ \text{grams of cereal}\rightarrow 1320\ \text{kJ}\)

\(\text{Exercise required}\) \(=\dfrac{1320}{1000}\times 30\)
  \(\approx 1.3\times 30\)
  \(\approx 40\ \text{minutes}\)

 
\(\Rightarrow B\)

Rates, SM-Bank 079 MC

Sandra is counting the cars heading south on the highway through her town.

She observes that 1 car passes every 6 seconds.

If Sandra is counting for 2 hours at this rate, how many cars does she count?

  1. 600
  2. 720
  3. 1200
  4. 1440
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\(C\)

Show Worked Solution

\(1\text{ car/}6\ \text{seconds}=10\text{ cars/}\text{minute}\)

\(\therefore\ \text{Cars in 2 hours}\) \(=2\times 10\times 60\)
  \(=1200\)

\(\Rightarrow C\)

Rates, SM-Bank 078

The hardware store is having a sale on ladders.

They make $1800 from selling 3 ladders.

All ladders on sale cost the same.

How much will the hardware store make if they sell 8 ladders?  (2 marks)

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\($4800\)

Show Worked Solution
\(\text{Price per ladder}\) \(=\dfrac{1800}{3}\)
  \(=$600\)

 

\(\text{Price of 8 ladders}\) \(=8\times $600\)
  \(=$4800\)

Rates, SM-Bank 075 MC

Esther can run 5 kilometres in 20 minutes.

Running at the same speed, how long will it take Esther to run 3 kilometres?

  1. 12
  2. 33
  3. 120
  4. 300
Show Answers Only

\(A\)

Show Worked Solution
\(\text{Minutes per kilometre}\) \(=\dfrac{20}{5}\)
  \(=4\)

 

\(\text{Minutes for 3 kilometres}\) \(=3\times 4\)
  \(=12\ \text{minutes}\)

\(\Rightarrow A\)

Rates, SM-Bank 072 MC

Gayle decorated 162 cookies in 9 hours.

What was her average decorating speed in cookies per hour?

  1. 18 cookies/hour
  2. 55 cookies/hour
  3. 153 cookies/hour
  4. 1458 cookies/hour
Show Answers Only

\(A\)

Show Worked Solution
\(\text{Average speed}\) \(=\dfrac{\text{Cookies decorated}}{\text{Time}}\)
  \(= \dfrac{162}{9}\)
  \(=18\ \text{cookies/hour}\)

\(\Rightarrow A\)

Rates, SM-Bank 069

An oyster farm sells bags of oysters in four different sizes.

Bag Size 1 kg 2 kg 3 kg 5 kg
Price $12.00 $23.10 $37.00 $55.00

What is the lowest price a customer can pay for 7 kg of oysters, given that you must buy whole bags?  (2 marks)

Show Answers Only

\($78.10\)

Show Worked Solution

\(\text{Calculate the cost per litre for each size:}\)

\(1\ \text{L}\) \(=$12.00\text{/kg}\)
\(2\ \text{L}\) \(= \dfrac{23.10}{2} =$11.55\text{/kg}\)
\(3\ \text{L}\) \(=\dfrac{37.00}{3} \approx $12.33\text{/kg}\)
\(5\ \text{L}\) \(=\dfrac{55.00}{5}= $11.00\text{/kg}\)

  

\(\therefore\ \text{Cheapest price to buy 7 kg}\)

\(=1\times 55.00+1\times 23.10\)

\(=$78.10\)

Rates, SM-Bank 068

A farmers' market sells olive oil in four different sizes.

Size 0.5 litre 1 litre 1.5 litres 3 litres
Price $3.75 $7.90 $11.70 $24.00

What is the lowest price a customer can pay for 6 litres of olive oil?  (2 marks)

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\($45.00\)

Show Worked Solution

\(\text{Calculate the cost per litre for each size:}\)

\(0.5\ \text{L}\) \(=$3.75\times 2=$7.50\text{/L}\)
\(1\ \text{L}\) \(= $7.90\text{/L}\)
\(1.5\ \text{L}\) \(=\dfrac{11.70}{1.5} = $7.80\text{/L}\)
\(3\ \text{L}\) \(=\dfrac{24.00}{3}= $8.00\text{/L}\)

  

\(\therefore\ \text{Cheapest price to buy 6 L}\)

\(=12\times 3.75\)

\(=$45.00\)

Rates, SM-Bank 067

A fish market sells prawns in four different sizes.

Size 0.5 kg 1 kg 2 kg 4 kg
Price $8.25 $16.30 $34.00 $65.50

What is the lowest price a customer can pay for 6 kg of prawns?  (2 marks)

Show Answers Only

\($97.80\)

Show Worked Solution

\(\text{Calculate the cost per kg for each size:}\)

\(0.5\text{kg}\) \(=$8.25\times 2=$16.50\text{/kg}\)
\(1\text{kg}\) \(= $16.30\text{/kg}\)
\(2\text{kg}\) \(=\dfrac{34.00}{2} = $17.00\text{/kg}\)
\(4\text{kg}\) \(=\dfrac{65.50}{4} \approx $16.38\text{/kg}\)

  

\(\therefore\ \text{Cheapest price to buy 6 kg}\)

\(=6\times 16.30\)

\(=$97.80\)

Rates, SM-Bank 066

A farmers' market sells potatoes in four different sizes.

Size 1 kg 2 kg 3 kg 5 kg
Price $3.40 $6.10 $9.30 $15.75

What is the lowest price a customer can pay for 8 kg of potatoes?  (2 marks)

Show Answers Only

\($24.40\)

Show Worked Solution

\(\text{Calculate the cost per kg for each size:}\)

\(1\text{kg}\) \(=$3.40\text{/kg}\)
\(2\text{kg}\) \(=\dfrac{6.10}{2} = $3.05\text{/kg}\)
\(3\text{kg}\) \(=\dfrac{9.30}{3} = $3.10\text{/kg}\)
\(4\text{kg}\) \(=\dfrac{15.75}{5} =$3.15\text{/kg}\)

 

\(\therefore\ 2\text{kg packet is the cheapest.}\)
 

\(\therefore\ \text{Cheapest price to buy 8 kg}\)

\(=4\times 6.10\)

\(=$24.40\)

Rates, SM-Bank 065

Juliette sets out to paddle her kayak from the railway bridge to the Riverside caravan park. Her average paddling speed was 10 kilometres per hour and she travelled 18 kilometres.

For how many hours and minutes did Juliette paddle?  (2 marks)

Show Answers Only

\(\text{1 hour and 48 minutes}\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(= \dfrac{18}{10}\)
  \(=1.8\ \text{hours}\)

 
\(\therefore \ \text{Juliette paddled for 1 hour and 48 minutes.}\)

Rates, SM-Bank 064

Mo drives 272 kilometres on the first leg of his holidays. His average speed was 64 kilometres per hour.

For how many hours and minutes was Mo driving?  (2 marks)

Show Answers Only

\(\text{4 hours and 15 minutes}\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(= \dfrac{272}{64}\)
  \(=4.25\ \text{hours}\)

 
\(\therefore \ \text{Mo travelled for 4 hours and 15 minutes.}\)

Rates, SM-Bank 063

Bart is driving a ski boat at an average speed of 40 km/h. He drives the boat for 1 and a quarter hours.

How far did Bart travel in the boat?  (2 marks)

Show Answers Only

\(50\ \text{km}\)

Show Worked Solution
\(\text{Distance}\) \(=\text{Speed}\times \text{Time}\)
  \(= 40\times 1.25\)
  \(=50\ \text{km}\)

 
\(\therefore \ \text{Bart travels 50 km}\)

Rates, SM-Bank 062

Miranda is walking an adventure trail at an average speed of 5 km/h. She completes the trail in 4.5 hours.

How far did Miranda walk?  (2 marks)

Show Answers Only

\(22.5\ \text{km}\)

Show Worked Solution
\(\text{Distance}\) \(=\text{Speed}\times \text{Time}\)
  \(= 5\times 4.5\)
  \(=22.5\ \text{km}\)

 
\(\therefore \ \text{Miranda walked 22.5 km}\)

Rates, SM-Bank 061

Donald hired a bike to ride around the zoo. He completed a circuit of all the exhibits in 2 hours and travelled 15 kilometres.

What was Donald's average speed?  (2 marks)

Show Answers Only

\(7.5\ \text{km/h}\)

Show Worked Solution
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
  \(= \dfrac{15}{2}\)
  \(=7.5\)

  \(\therefore \ \text{Donald’s average speed was 7.5 km/h.}\)

Rates, SM-Bank 060

Jory drives his car to work 120 km away. It takes him 2 hours to complete the trip.

What was his average speed for the trip?  (2 marks)

Show Answers Only

\(60\ \text{km/h}\)

Show Worked Solution
\(\text{Speed}\) \(=\dfrac{\text{Distance}}{\text{Time}}\)
  \(= \dfrac{120}{2}\)
  \(=60\)

  \(\therefore \ \text{Jory was travelling at 60 km/h.}\)

Rates, SM-Bank 059

An avocado farmer sells her avocados in four different sizes.

Size 1 kg 2 kg 3 kg 4 kg
Price $6.35 $13.00 $19.00 $25.10

What is the lowest price a customer can pay for 8 kg of avocados?  (2 marks)

Show Answers Only

\($50.20\)

Show Worked Solution

\(\text{Calculate the cost per kg for each size:}\)

\(1\text{kg}\) \(=$6.35\text{/kg}\)
\(2\text{kg}\) \(=\dfrac{13}{2} = $6.50\text{/kg}\)
\(3\text{kg}\) \(=\dfrac{19}{3} = $6.33\text{/kg}\)
\(4\text{kg}\) \(=\dfrac{25.10}{4} \approx $6.28\text{/kg}\)

 

\(\therefore\ 4\text{kg packet is the cheapest.}\)
 

\(\therefore \text{Cheapest price to buy 8 kg}\)

\(=2\times 25.10\)

\(=$50.20\)

Rates, SM-Bank 058 MC

A shop sells four sizes of chocolate bar. 

 

 Which packet costs the least per gram?

  1. Packet 1
  2. Packet 2
  3. Packet 3
  4. Packet 4
Show Answers Only

\(B\)

Show Worked Solution
\(\text{Packet 1}\) \(=\dfrac{288}{200} = 1.44\ \text{c/g}\)
\(\text{Packet 2}\) \(=\dfrac{310}{220} = 1.41\ \text{c/g}\)
\(\text{Packet 3}\) \(=\dfrac{181}{125} = 1.45\ \text{c/g}\)
\(\text{Packet 4}\) \(=\dfrac{497}{350} = 1.42\ \text{c/g}\)

 

\(\therefore\ \text{Packet 2 costs the least per gram.}\)
 

\(\Rightarrow B\)

Rates, SM-Bank 055

Jesse sells, an average of 150 roller-coaster tickets every 10 minutes.  How long will it take him sell 600 tickets?  (2 marks)

Show Answers Only

\(40\ \text{minutes}\)

Show Worked Solution
\(10\ \text{minutes}/150\ \text{tickets}\) \(=\dfrac{10}{150}\ \text{minutes}/\dfrac{150}{150}\ \text{tickets}\)
  \(=\dfrac{1}{15}\ \text{minute}/1\ \text{ticket}\)
  \(=\bigg(\dfrac{1}{15}\times 600\bigg)\ \text{minutes}/600\ \text{tickets}\)
  \(=40\ \text{minutes}/600\ \text{tickets}\)

 
\(\therefore\ \text{It would take}\ 40\ \text{minutes to sell}\ 600\ \text{tickets.}\)

Rates, SM-Bank 048

Zach is saving money every year. The graph shows how much money is in his bank account at the end of each year.
 


 

What was Zach's average amount of money saved per year during the first 5 years?  (2 marks)

Show Answers Only

\($120\text{/year}\)

Show Worked Solution
\(\text{Average saved per year}\) \(=\dfrac{\text{Money at Y5}}{\text{time}}\)
  \(= \dfrac{600}{5}\)
  \(= $120\text{/year}\)

Rates, SM-Bank 047

Peter went on a 150 kilometre drive to the lake. The graph below shows the distance driven, in kilometres, and the time, in hours, taken for the trip.
 

 

What was the average speed of Peter's car during the first 6 hours?  (2 marks)

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\(20\ \text{km/h}\)

Show Worked Solution
\(\text{Average speed for first 6 hrs}\) \(=\dfrac{\text{Distance at 6 hours}}{\text{time}}\)
  \(= \dfrac{120}{6}\)
  \(= 20\ \text{km/h}\)

Rates, SM-Bank 045 MC

Barry lives 30 kilometres from the library.

On Tuesday, he drove to the library and averaged 90 kilometres per hour.

On Thursday, he took the train which averaged 30 kilometres per hour.

What was the extra time of the train journey, in minutes, compared to when he drove on Tuesday?

  1. \(20\)
  2. \(30\)
  3. \(40\)
  4. \(60\)
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\(C\)

Show Worked Solution
\(\text{Time Driving}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(= \dfrac{30}{90}\)
  \(= \dfrac{1}{3}\ \text{hour}\)
  \(=20\ \text{minutes}\)

 

\(\text{Train Time}\) \(=\dfrac{30}{30}\)
  \(= 1\ \text{hour}\)
  \(= 60\ \text{minutes}\)

 

\(\therefore\ \text{The extra time taking the train}\)

\(=60-20\)

\(= 40\ \text{minutes}\)

 
\(\Rightarrow C\)

Rates, SM-Bank 044 MC

Fleur lives 15 kilometres from her work.

On Wednesday, she drove to work and averaged 60 kilometres per hour.

On Thursday, she took the bus which averaged 15 kilometres per hour.

What was the extra time of the bus journey, in minutes, compared to when she drove on Wednesday?

  1. \(15\)
  2. \(45\)
  3. \(60\)
  4. \(75\)
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\(B\)

Show Worked Solution
\(\text{Time on Wednesday}\) \(=\dfrac{15}{60}\)
  \(= 0.25\ \text{hour}\)
  \(= 15\ \text{minutes}\)

 

\(\text{Time on Thursday}\) \(=\dfrac{15}{15}\)
  \(= 1\ \text{hour}\)
  \(= 60\ \text{minutes}\)

 

\(\therefore\ \text{The extra time taking the bus}\)

\(=60-15\)

\(= 45\ \text{minutes}\)

 
\(\Rightarrow B\)

Rates, SM-Bank 043 MC

Elvis walks from his home to the beach through a park.
 

  
Which of the following situations best fits the distance/time graph above, where distance is Elvis' distance from home?

  1. Elvis ran to the park, sat down on a bench, and then ran home.
  2. Elvis walked to the park, sat down on a bench, then ran to the beach.
  3. Elvis ran to the beach, sat down, then ran home.
  4. Elvis walked to the park, sat down on a bench, then walked to the beach.
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\(D\)

Show Worked Solution

\(\text{The horizontal section of the graph indicates Elvis’ distance}\)

\(\text{from home is not changing and he is resting.}\)

\(\text{The slope before and after the rest break is the same, so Elvis’}\)

\(\text{speed of travel was the same before and after the rest.}\)

 

\(\therefore\ \text{Elvis walked, rested then walked.}\)

 
\(\Rightarrow D\)

Rates, SM-Bank 042 MC

Columbo had a full drum of water.
 

 
  

He put two holes in the bottom and the water began leaking out.

After a few minutes, Columbo closed off one of the holes in the drum and the water poured out more slowly.

Which graph below best shows the depth of water in the drum against time?

  
A. B. C. D.
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\(B\)

Show Worked Solution

\(\text{The depth decreases quickly at a constant rate at the start}\)

\(\text{(steep decline) and then slows down when one hole is }\)

\(\text{closed (less steep decline).}\)

\(\Rightarrow B\)

Rates, SM-Bank 041 MC

Kelly drives her motorised scooter to the shopping centre 9 km away at an average speed of 45 km per hour.

How long does the trip take?

  1. 5 minutes
  2. 12 minutes
  3. 24 minutes
  4. 40.5 minutes
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\(B\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(= \dfrac{9}{45}\)
  \(= \dfrac{1}{5}\ \text{hours}\)
  \(=12\ \text{minutes}\)

 
\(\Rightarrow B\)

Rates, SM-Bank 040 MC

Kingsley drives her moped to a beach 100 km away at an average speed of 60 km.

How long does the trip take?

  1. 36 minutes
  2. 1 hour 20 minutes
  3. 1 hour 24 minutes
  4. 1 hour 40 minutes
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\(D\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(= \dfrac{100}{60}\)
  \(= 1\dfrac{40}{60}\ \text{hours}\)
  \(=1\ \text{hour}\ 40\ \text{minutes}\)

 
\(\Rightarrow D\)

Rates, SM-Bank 039 MC

Lachlan drives his boat to an island 100 km away at an average speed of 80 km/h.

How long does the trip take?

  1. 48 minutes
  2. 1 hour 15 minutes 
  3. 1 hour 20 minutes 
  4. 1 hour 30 minutes 
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\(B\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{\text{Speed}}\)
  \(= \dfrac{100}{80}\)
  \(= 1.25\ \text{hours}\)
  \(=1\ \text{hour}\ 15\ \text{minutes}\)

 
\(\Rightarrow B\)

Rates, SM-Bank 038

Ant is travelling at 110 km/h in his car.

If he maintains this speed, how many kilometres will he travel in 1 hour and 20 minutes?  Give your answer correct to the nearest kilometre.   (2 marks)

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\(147\ \text{km}\)

Show Worked Solution
\(\text{Distance}\) \(=\text{Speed}\times \text{time}\)
  \(= 110\times \dfrac{80}{60}\)
  \(= 110\times \dfrac{4}{3}\)
  \(= 146.\dot{6}\ \text{km}\)
  \(=147\ \text{km  (nearest km)}\)

Rates, SM-Bank 037

Vicki is travelling at 90 km/h in her car.

If she maintains this speed, how many kilometres will she travel in 35 minutes?  (2 marks)

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\(52.5\ \text{km}\)

Show Worked Solution
\(\text{Distance}\) \(=\text{Speed}\times \text{time}\)
  \(= 90\times \dfrac{35}{60}\)
  \(= 90\times \dfrac{7}{12}\)
  \(= 52.5\ \text{km}\)