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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 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 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
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\(A\)

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
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\(A\)

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

\(\Rightarrow A\)

Rates, SM-Bank 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)

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

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)

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

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)

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\(50\ \text{km}\)

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)

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\(22.5\ \text{km}\)

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)

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

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)

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

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

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)

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\(35\ \text{km}\)

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)

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\(80\ \text{km}\)

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 016

Riley lives 3 km from the park.

He jogs at a constant speed of 10 km per hour.

How many minutes does it take for Riley to get to the park?  (2 marks)

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\(18\ \text{minutes}\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{Distance}}{{\text{S}\text{peed}}}\)
  \(=\dfrac{3}{10}\ \text{hr}\)
  \(=\dfrac{3}{10}\times 60\)
  \(=18\ \text{minutes}\)

Rates, SM-Bank 015

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?  (2 marks)

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\(45\ \text{minutes}\)

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

 

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

 

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

\(=60-15\)

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

Rates, SM-Bank 013

Johnno was standing 300 metres away from the stage at a rock concert.

If the sound travelled at 330 metres per second from the stage, how many seconds did the sound take to get to Johnno? Give your answer correct to 2 decimal places.  (2 marks)

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\(0.91\ \text{seconds}\)

Show Worked Solution
\(\text{Time}\) \(=\dfrac{\text{distance}}{\text{speed}}\)
  \(= \dfrac{300}{330}\)
  \(= 0.909090…\approx 0.91\ \text{(2 d.p.)}\)

  
\(\therefore \text{The sound takes approximately}\ 0.91\ \text{seconds to reach Johnno.}\)

Rates, SM-Bank 012

Rhonda rode her hovercraft at a speed of 5 metres per second.

If she rode for 3 minutes, how far did she go?  (2 marks)

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\(\text{900}\ \text{m}\)

Show Worked Solution
\(3\ \text{minutes}\) \(=60\times 3\ \text{seconds}\)
  \(=180\ \text{seconds}\)

 

\(\text{Distance}\) \(=\text{Speed}\times\text{Time}\)
  \(= 5\times 180\)
  \(= 900\ \text{m}\)