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Exam questions · Maths · Ratio and Proportion

Speed, Distance, Time and Density

  • 6 exam questions
  • 17 marks
  • 9 quick checks
  1. 1 Work out [2 marks]

    A train travels 210 km in 3 hours 30 minutes. Work out the average speed of the train.

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    Model answer

    3 hours 30 minutes is 3.5 hours, so the speed is \(210 \div 3.5 = 60\) km/h.

    Mark scheme

    • \(210 \div 3.5\) or 3.5 hours seen — M1
    • 60 km/h — A1
  2. 2 Work out [2 marks]

    A runner runs at 12 km/h for 1 hour 45 minutes. How far does the runner run?

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    Model answer

    1 hour 45 minutes is 1.75 hours, so the distance is \(12 \times 1.75 = 21\) km.

    Mark scheme

    • \(12 \times 1.75\) or 1.75 hours seen — M1
    • 21 km — A1
  3. 3 Work out [5 marks]

    The graph shows Sofia's journey from her home to a campsite. (a) How far had Sofia travelled when she stopped? [1 mark] (b) Work out Sofia's speed during the last part of her journey. [2 marks] (c) Work out Sofia's average speed for the first 2 hours of her journey. [2 marks]

    A distance-time graph of a journey: 45 km in the first hour, a stop of one hour, then a steady journey reaching 150 km after 5 hours.
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    Model answer

    (a) The flat part of the graph is at 45 km. (b) In the last part she travelled \(150 - 45 = 105\) km in \(5 - 2 = 3\) hours, so her speed was \(105 \div 3 = 35\) km/h. (c) In the first 2 hours she travelled 45 km, so her average speed was \(45 \div 2 = 22.5\) km/h.

    Mark scheme

    • (a) 45 km — B1
    • (b) \(105 \div 3\) — M1
    • (b) 35 km/h — A1
    • (c) \(45 \div 2\) — M1
    • (c) 22.5 km/h — A1
  4. 4 Work out [2 marks]

    Jess walks 6 km in 90 minutes. Work out her average speed in kilometres per hour.

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    Model answer

    90 minutes is 1.5 hours, so the speed is \(6 \div 1.5 = 4\) km/h.

    Mark scheme

    • \(6 \div 1.5\) or 1.5 hours seen — M1
    • 4 km/h — A1
  5. 5 Work out [2 marks]

    A solid has a mass of 450 g and a volume of 60 cm\(^3\). Work out the density of the solid.

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    Model answer

    Density \(=\) mass \(\div\) volume \(= 450 \div 60 = 7.5\) g/cm\(^3\).

    Mark scheme

    • \(450 \div 60\) — M1
    • 7.5 g/cm\(^3\) — A1
  6. 6 Work out [4 marks]

    (a) A car travels at 90 km/h. Work out this speed in metres per second. [2 marks] (b) A force of 240 N acts on an area of 0.4 m\(^2\). Work out the pressure in N/m\(^2\). [2 marks]

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    Model answer

    (a) \(90 \times 1000 \div 3600 = 25\) m/s. (b) Pressure \(= 240 \div 0.4 = 600\) N/m\(^2\).

    Mark scheme

    • (a) \(90 \times 1000 \div 3600\) or \(90 \div 3.6\) — M1
    • (a) 25 — A1
    • (b) \(240 \div 0.4\) — M1
    • (b) 600 — A1

Quick check

  1. 1

    A car travels 150 km in 2 hours 30 minutes. What is its average speed?

    1. A375 km/h
    2. B75 km/h
    3. C50 km/h
    4. D60 km/h
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    D: 60 km/h

    Write 2 hours 30 minutes as 2.5 hours. Then \(150 \div 2.5 = 60\) km/h.

  2. 2

    What is 45 minutes as a decimal of an hour?

    1. A0.45 hours
    2. B4.5 hours
    3. C0.75 hours
    4. D1.25 hours
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    C: 0.75 hours

    \(45 \div 60 = 0.75\).

  3. 3

    A train travels at 80 km/h for 3 hours 15 minutes. How far does it go?

    1. A252 km
    2. B260 km
    3. C240 km
    4. D320 km
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    B: 260 km

    3 hours 15 minutes is 3.25 hours, so the distance is \(80 \times 3.25 = 260\) km. Writing the time as 3.15 hours is a common error.

  4. 4

    A cyclist rides 60 km at 30 km/h and then 60 km at 60 km/h. What is the average speed for the whole journey?

    1. A40 km/h
    2. B45 km/h
    3. C50 km/h
    4. D90 km/h
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    A: 40 km/h

    The times are 2 hours and 1 hour. The total distance is 120 km and the total time is 3 hours, so \(120 \div 3 = 40\) km/h.

  5. 5

    What does a horizontal line on a distance-time graph show?

    1. AThe object has constant speed
    2. BThe object is speeding up
    3. CThe object is returning to the start
    4. DThe object is stationary
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    D: The object is stationary

    A flat line means the distance is not changing with time, so the speed is zero.

  6. 6

    A metal block has mass 240 g and volume 30 cm\(^3\). What is its density?

    1. A7200 g/cm\(^3\)
    2. B0.125 g/cm\(^3\)
    3. C8 g/cm\(^3\)
    4. D270 g/cm\(^3\)
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    C: 8 g/cm\(^3\)

    Density \(=\) mass \(\div\) volume \(= 240 \div 30 = 8\) g/cm\(^3\).

  7. 7

    The density of a metal is 8 g/cm\(^3\). What is the mass of 25 cm\(^3\) of it?

    1. A3.125 g
    2. B200 g
    3. C33 g
    4. D0.32 g
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    B: 200 g

    Mass \(=\) density \(\times\) volume \(= 8 \times 25 = 200\) g.

  8. 8

    Change 72 km/h into metres per second.

    1. A20 m/s
    2. B259.2 m/s
    3. C72 000 m/s
    4. D1.2 m/s
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    A: 20 m/s

    \(72 \times 1000 = 72\,000\) m per hour, and \(72\,000 \div 3600 = 20\) m/s.

  9. 9

    A force of 600 N acts on an area of 0.5 m\(^2\). What is the pressure?

    1. A300 N/m\(^2\)
    2. B600.5 N/m\(^2\)
    3. C0.0008 N/m\(^2\)
    4. D1200 N/m\(^2\)
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    D: 1200 N/m\(^2\)

    Pressure \(=\) force \(\div\) area \(= 600 \div 0.5 = 1200\) N/m\(^2\).