SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

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)

Show Answers Only

\($45.00\)

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 052

Convert 16 metres per second into kilometres per hour. (2 marks)

Show Answers Only

\(57.6\ \text{km/hour}\)

Show Worked Solution
\(16\ \text{m/second}\) \(=(16\times 60\times 60)\ \text{m/hour}\)
  \(=57\ 600\ \text{m/hour}\)
  \(=57.6\ \text{km/hour}\)

Rates, SM-Bank 056

Convert $648 per hour into cents per second. (2 marks)

Show Answers Only

\(18\ \text{cents/second}\)

Show Worked Solution
\($648\text{/hour}\) \(=\bigg(\dfrac{64\ 800}{60\times 60}\bigg)\ \text{cents/second}\)
  \(=18\ \text{cents/second}\)

Rates, SM-Bank 051

Convert 15 grams per day into kilograms per week. (2 marks)

Show Answers Only

\(0.105\ \text{kg/}\text{week}\)

Show Worked Solution
\(15\ \text{g/day}\) \(=15\times 7\ \text{g/week}\)
  \(=105\ \text{g/}\text{week}\)
  \(=0.105\ \text{kg/}\text{week}\)

Rates, SM-Bank 049

Convert $30 per hour into cents per minute. (2 marks)

Show Answers Only

\(50\ \text{cents/}\text{minute}\)

Show Worked Solution
\($30\text{/hour}\) \(=3000\ \text{cents/}60\ \text{minutes}\)
  \(= \dfrac{3000}{60}\ \text{cents/}\dfrac{60}{60}\ \text{minutes}\)
  \(=50\ \text{cents/}\text{minute}\)

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)

Show Answers Only

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

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. \(60\)
Show Answers Only

\(C\)

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. \(75\)
Show Answers Only

\(B\)

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.
Show Answers Only

\(D\)

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.
Show Answers Only

\(B\)

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
Show Answers Only

\(B\)

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
Show Answers Only

\(D\)

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 
Show Answers Only

\(B\)

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)

Show Answers Only

\(147\ \text{km}\)

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)

Show Answers Only

\(52.5\ \text{km}\)

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

Rates, SM-Bank 036

Joy is travelling at 42 km/h on her racing bike.

If she maintains this speed, how many kilometres will she travel in 50 minutes?  (2 marks)

Show Answers Only

\(35\ \text{km}\)

Show Worked Solution
\(\text{Distance}\) \(=\text{Speed}\times \text{time}\)
  \(= 42\times \dfrac{50}{60}\)
  \(= 42\times \dfrac{5}{6}\)
  \(= 35\ \text{km}\)

Rates, SM-Bank 035

Billy Bob is travelling at 120 km/h in his car.

If he maintains this speed, how many kilometres will he travel in 40 minutes?  (2 marks)

Show Answers Only

\(80\ \text{km}\)

Show Worked Solution
\(\text{Distance}\) \(=\text{Speed}\times \text{time}\)
  \(= 120\times \dfrac{40}{60}\)
  \(= 120\times \dfrac{2}{3}\)
  \(= 80\ \text{km}\)

Rates, SM-Bank 034

Aurora works part time in a donut shop.

On weekends, she earns 2.5 times as much per hour as she earns on weekdays.

One week, she works 14.5 hours on weekdays and 3 hours on the weekend.

Her pay for the week was $319.

How much does she earn in 1 hour on a weekday?  (2 marks)

Show Answers Only

\($12.50/\text{hour}\)

Show Worked Solution
\(\text{Pay hours}\) \(= 14.5+3\times 2.5\)
  \(=22\)

 

\(\text{Earnings for 1 hour}\) \(=\dfrac{319}{22}\)
  \(=$14.50\)

 
\(\therefore \text{Aurora earns}\ $14.50\ \text{in 1 hour.}\)

Rates, SM-Bank 033

Fleur works part time in a flower shop.

On weekends, she earns 2 times as much per hour as she earns on weekdays.

One week, she works 23 hours on weekdays and 1.5 hours on the weekend.

Her pay for the week was $351.

How much does she earn in 1 hour on a weekday?  (2 marks)

Show Answers Only

\($13.50/\text{hour}\)

Show Worked Solution
\(\text{Pay hours}\) \(= 23+2\times 1.5\)
  \(=26\)

 

\(\text{Earnings for 1 hour}\) \(=\dfrac{351}{26}\)
  \(=$13.50\)

 
\(\therefore \text{Fleur earns}\ $13.50\ \text{in 1 hour.}\)

Rates, SM-Bank 032

Fanny works part time at Guzman y Gomez.

On weekends, she earns 1.5 times as much per hour as she earns on weekdays.

One week, she works 12 hours on weekdays and 8 hours on the weekend.

Her pay for the week was $414.

How much does she earn in 1 hour on a weekday?  (2 marks)

Show Answers Only

\($17.25/\text{hour}\)

Show Worked Solution
\(\text{Pay hours}\) \(= 12+ 8 \times 1.5\)
  \(=24\)

 

\(\text{Earnings for 1 hour}\) \(=\dfrac{414}{24}\)
  \(=$17.25\)

Rates, SM-Bank 031

Clay has a casual job at the local movie cinema.

On weekends, he earns 1.5 times as much per hour as he earns on weekdays.

One week, he works 20 hours on weekdays and 6 hours on the weekend.

His pay for the week was $498.80.

How much does he earn in 1 hour on a weekday?  (2 marks)

Show Answers Only

\($17.20/\text{hour}\)

Show Worked Solution
\(\text{Pay hours}\) \(= 20+6\times 1.5\)
  \(=29\)

 

\(\text{Earnings for 1 hour}\) \(=\dfrac{498.80}{29}\)
  \(=$17.20\)

 
\(\therefore \text{Clay earns}\ $17.20\ \text{in 1 hour.}\)

Rates, SM-Bank 030

Betty works part time in a clothing shop.

On weekends, she earns 2 times as much per hour as she earns on weekdays.

One week, she works 15 hours on weekdays and 3 hours on the weekend.

Her pay for the week was $367.50.

How much does she earn in 1 hour on a weekday?  (2 marks)

Show Answers Only

\($17.50/\text{hour}\)

Show Worked Solution
\(\text{Pay hours}\) \(= 15+3\times 2\)
  \(=21\)

 

\(\text{Earnings for 1 hour}\) \(=\dfrac{367.50}{21}\)
  \(=$17.50\)

 
\(\therefore \text{Betty earns}\ $17.50\ \text{in 1 hour.}\)

Rates, SM-Bank 029

Brin works part time in a coffee shop.

On weekends, he earns 1.5 times as much per hour as he earns on weekdays.

One week, he works 9 hours on a weekday and 4 hours on the weekend.

His pay for the week was $270.

How much does he earn in 1 hour on a weekday?  (2 marks)

Show Answers Only

\($18/\text{hour}\)

Show Worked Solution
\(\text{Pay hours}\) \(= 9+4\times 1.5\)
  \(=15\)

 

\(\text{Earnings for 1 hour}\) \(=\dfrac{270}{15}\)
  \(=$18\)

 
\(\therefore \text{Brin earns}\ $18\ \text{in 1 hour.}\)

Rates, SM-Bank 028

John's old tractor used 8.3 litres of fuel per 100km.

His new tractor uses 5.9 litres of fuel per 100 km.

John pays $2.15 per litre for fuel and drives 20,000 km each year.

How much money will John save on fuel each year with his new tractor?  (2 marks)

Show Answers Only

\($1032\)

Show Worked Solution

\(\text{Fuel cost of old tractor}\)

\(=8.3\times $2.15\times \dfrac{20\ 000}{100}\)

\(=8.3\times $2.15\times 200\)

\(=$3569\)
 

\(\text{Fuel cost of new tractor}\)

\(=5.9\times $2.15\times\dfrac{20\ 000}{100}\)

\(=5.9\times $2.15\times 200\)

\(=$2537\)

 

\(\therefore\ \text{John’s fuel savings each year}\)

\(=$3569-$2537\)

\(=$1032\)

Rates, SM-Bank 027

One litre of softdrink contains 90 grams of sugar.

How many millilitres of softdrink contain 4.5 grams of sugar?  (2 marks)

Show Answers Only

\( 50\ \text{mL}\)

Show Worked Solution
\(\text{Millilitres}\) \(= \dfrac{4.5}{90}\times 1000\ \text{mL}\)
  \(= 50\ \text{mL}\)

Rates, SM-Bank 026

Kurt is travelling from Newcastle to Sydney. The journey is 165 kilometres.

His car uses 8.35 litres of fuel per 100 kilometres.

How much fuel will Kurt need to make the journey?

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

Show Answers Only

\(14\ \text{litres (nearest whole number)}\)

Show Worked Solution
\(\text{Fuel needed}\) \(=\dfrac{165}{100}\times 8.35\)
  \(= 13.77\dots\)
  \(= 14\ \text{litres (nearest whole number)}\)

Rates, SM-Bank 025

A laundromat can wash 12 loads of laundry in one hour at full capacity.

A standard load of laundry weighs 7 kilograms.

Here is some information about two different washing machines.
 

Washing machine

Amount of water used per
kilogram of laundry (litres)
Top loader 10.25
Front loader 6.5

 
Working at full capacity, how many litres of water would the laundromat expect to save in one hour by using the front loader instead of the top loader?  (2 marks)

Show Answers Only

\(315\ \text{L}\)

Show Worked Solution

\(\text{Top loader water used (1 load)}\)

\(= 7\times 10.25\)

\(= 71.75\ \text{L}\)
 

\(\text{Front loader water used (1 load)}\)

\(= 7\times 6.5\)

\(= 45.5\ \text{L}\)
 

\(\therefore\ \text{Expected water saved}\)

\(= 12\times (71.75-45.5)\)

\(= 315\ \text{L}\)

Rates, SM-Bank 024

Gary used 4 litres of paint to paint a wall.

The wall was a rectangle 2 metres high and 3 metres wide.

How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 5 metres wide?  (2 marks)

Show Answers Only

\(10\)

Show Worked Solution

\(\text{Area of smaller wall}\)

\(= 2\times 3\)

\(= 6\ \text{m}^2\)

 

\(\text{S}\text{ince 4 litres of paint are needed to}\)

\(\text{paint the small wall:}\)

\(\rightarrow\ \text{Paint needed for 1 m}^2\)

\(= \dfrac{4}{6}\)

\(= \dfrac{2}{3}\ \text{litre}\)

\(\rightarrow\ \text{Area of larger wall}\)

\(= 3\times 5\)

\(= 15\ \text{m}^2\)

 

\(\text{Paint needed}\) \(= 15\times \dfrac{2}{3}\)
  \(= 10\ \text{litres}\)

Rates, SM-Bank 023

Genghis and Kublai are shooting arrows at a target.

Genghis shoots an arrow every 3 seconds.

Kublai shoots an arrow every 8 seconds.

They shoot their first arrow together at 10:00 am.

How many more times will they shoot arrows at exactly the same time in the next 3 minutes?  (2 marks)

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\(7\)

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\(\text{Lowest common multiple of 3 and 8}=24\)

\(\therefore\ \text{Every 24 seconds, the arrows are shot at the same time.}\)

\(\rightarrow\ \text{Arrows are shot at the same time:}\)

\(24, 48, 72, 96, 120, 144, 168\ \text{seconds}\)

\(\therefore\ 7\ \text{more times  (time ≤ 180 seconds)}\)

Rates, SM-Bank 022

Patrick uses 25 litres of water every minute when he has a shower.

Kate uses 150 litres of water when she has a bath.

How many fewer litres of water does Patrick use in his 5½ minute shower than Kate does in her bath?  (2 marks)

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\(12.5\ \text{litres}\)

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\(\text{Patrick water usage}\)

\(= 5.5\times 25\)

\(= 137.5\ \text{litres}\)
 

\(\therefore\ \text{Less litres}\)

 \(= 150-137.5\)
  \(=12.5\ \text{litres}\)

Rates, SM-Bank 021

Kate buys a new computer.

The disk in its hard drive makes 120 full turns every second.

How many minutes will it take for the disk to make 324 000 full turns?  (2 marks)

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\(45\ \text{minutes}\)

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\(\text{Turns in 1 minute}\)

\(= 120\times 60\)

\(= 7200\)
 

\(\therefore\ \text{Minutes needed}\)

\(= \dfrac{324\ 000}{7200}\)

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

Rates, SM-Bank 018

A solar panel grid on a school roof produces an average of 8.6 kWh of energy per day.

How much energy will the grid produce for the school on average over 7 days?  (2marks)

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\(60.2\ \text{kWh}\)

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\(\text{One multiplication strategy:}\)

\(7\times 8=56\)

\(7\times 0.6 = 4.2\)

\(7\times 8.6 = 56+4.2=60.2\)
 

\(\therefore\ \text{It produces 60.2 kWh over 7 days.}\)