[discia] GCSE Maths › Ratio and Proportion › Speed and Density

Speed and Density

discia.org 10 questions · 34 marks
Name Date
  1. Either paper 4 marks

    A lorry travels along a motorway at a steady speed.

    12345501001502002500time (hours)distance (km)
    (a)

    Calculate the speed of the lorry. Give your answer in kilometres per hour.

    (b)

    The lorry keeps going at the same speed.

    Work out how long it takes the lorry to travel \(350\) km.

    Show answer
    (a) \(50\ \text{km/h}\)
    (b) \(7\ \text{hours}\)
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  2. Either paper 3 marks
    Two solids, J and K, have the same density.
    JK
    Mass108
    Volume122
    Density
    Complete the table. Include units in your answers.
    Show answer
    Density \(9\) g/cm³ (both cells); Block K's missing mass is \(18\) g
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  3. Either paper 2 marks

    No real values are given in this question.

    (a)

    The distance of journey \(A\) is 9 times the distance of journey \(B\), and its time is 12 times the time of journey \(B\).

    Complete the sentence. The average speed of journey \(A\) is ______ times the average speed of journey \(B\).

    (b)

    For a journey, the distance is multiplied by 5 and the time is divided by 4.

    What happens to the average speed? Circle your answer.

    multiplied by 5/4

    multiplied by 20

    multiplied by 4/5

    divided by 20

    no change

    Show answer
    (a) \(3/4\)
    (b) multiplied by 20
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  4. Either paper 3 marks

    A cuboid of copper has length \(14\) cm, width \(4\) cm and height \(8\) cm. The copper has a density of \(9\) g/cm\(^3\).

    Find the mass of the cuboid in grams.

    Show answer
    \(4032\ \text{g}\)
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  5. Either paper 3 marks

    A lorry travels \(54\) km at an average speed of \(30\) km/h.

    Calculate how long the lorry takes to travel this distance.

    Give your answer in hours and minutes.

    Show answer
    \(1\) hour \(48\) minutes
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  6. Either paper 3 marks

    Sam and Priya are two runners in a 216-metre race.

    Sam completes the race in 29 seconds.

    Priya's average speed for the race is 28.8 kilometres per hour.

    Who wins the race? You must show your working.

    Show answer
    Priya wins the race - Sam takes 29 s and Priya takes 27 s.
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  7. Either paper 6 marks

    Ben cycles 144 m in 48 seconds at a constant speed.

    (a)

    On another day, he cycles \(4.5\) km, assuming the same speed as before.

    Calculate how long this takes. Give your answer in minutes.

    (b)

    In fact, on the second day Ben cycled at a slower speed than on the first day.

    Is the time he actually took:

    less than the answer to part (a)

    the same as the answer to part (a)

    greater than the answer to part (a)

    not possible to say

    Tick the correct answer.

    Show answer
    (a) \(25\ \text{minutes}\)
    (b) greater than the answer to part (a)
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  8. Either paper 3 marks

    A car makes a journey of \(220\) miles in \(4\) hours 10 minutes.

    For the first \(100\) miles of the journey the average speed of the car is \(60\) mph.

    Find the average speed of the car for the rest of the journey.

    Show answer
    \(48\ \text{mph}\)
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  9. Either paper 4 marks

    A, B, C and D are junctions on a motorway, in that order.

    ABCDBC = 20 miles CD = 2 × AB (not drawn to scale)

    Callum drives from A to C. He drives for \(30\) minutes at an average speed of \(60\) miles per hour.

    Work out the distance AD.

    Show answer
    \(50\ \text{miles}\)
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  10. Either paper 3 marks

    The first stage of a journey takes \(2\) hours at an average speed of \(75\) km/h. The second stage takes \(3\) hours at an average speed of \(45\) km/h.

    Work out the average speed for the whole journey.

    Show answer
    \(57\ \text{km/h}\)
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discia.org Speed and Density · sheet 1
Answers Speed and Density · sheet 1
  1. (a) \(50\ \text{km/h}\)
    (b) \(7\ \text{hours}\)
  2. Density \(9\) g/cm³ (both cells); Block K's missing mass is \(18\) g
  3. (a) \(3/4\)
    (b) multiplied by 20
  4. \(4032\ \text{g}\)
  5. \(1\) hour \(48\) minutes
  6. Priya wins the race - Sam takes 29 s and Priya takes 27 s.
  7. (a) \(25\ \text{minutes}\)
    (b) greater than the answer to part (a)
  8. \(48\ \text{mph}\)
  9. \(50\ \text{miles}\)
  10. \(57\ \text{km/h}\)
discia.org Speed and Density · sheet 1