[discia] GCSE Maths › Algebra › Real Life and Distance Time Graphs

Real Life and Distance Time Graphs

discia.org 10 questions · 37 marks
Name Date
  1. Either paper 3 marks

    Reuben cycles along a straight road at a steady speed.

    The distance-time graph shows the first \(30\) seconds of the journey.

    time (s)distance (m)510152025302550751000
    (a)

    How far had Reuben travelled after \(5\) seconds?

    (b)

    Work out Reuben's speed. Give your answer in metres per second.

    Show answer
    (a) \(15\ \text{m}\)
    (b) \(3\ \text{m/s}\)
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  2. Either paper 3 marks

    Amara drives a delivery van away from the depot, stops to make a delivery, then drives further on to a second delivery.

    time (minutes)distance from the depot (km)102030405060708090246810121416180
    (a)

    For how many minutes was the van stopped at the first delivery?

    (b)

    How far was the van from the depot at the end of the journey?

    (c)

    Between \(40\) minutes and \(50\) minutes the graph is horizontal.

    Write down what this tells you about the van.

    Show answer
    (a) \(10\ \text{minutes}\)
    (b) \(16\ \text{km}\)
    (c) The van was not moving. It stayed 8 km from the depot while the delivery was made.
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  3. Either paper 5 marks

    Erin drives from home to a garden centre, stays there for a while, then drives straight home again.

    time (minutes)distance from home (km)102030405060708090100102030400
    (a)

    For how many minutes did Erin stay at the garden centre?

    (b)

    Work out Erin's speed on the journey to the garden centre.

    Give your answer in kilometres per hour.

    (c)

    The journey there and the journey home cover the same distance.

    Which of the two was faster?

    Show answer
    (a) \(10\ \text{minutes}\)
    (b) \(45\ \text{km/h}\)
    (c) The outward journey
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  4. Either paper 4 marks

    A train travels from Derby to Nottingham at a steady speed.

    The distance axis is numbered every \(20\) km, with a smaller square every \(5\) km.

    time (minutes)distance (km)102030405060204060801001200
    (a)

    Use the graph to work out how far the train had travelled after \(30\) minutes.

    (b)

    Work out the average speed of the train.

    Give your answer in kilometres per hour.

    Show answer
    (a) \(50\ \text{km}\)
    (b) \(100\ \text{km/h}\)
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  5. Either paper 5 marks

    Two runners set off together and each runs at a steady speed for \(40\) seconds.

    Runner \(X\) and runner \(Y\) are shown on the same grid.

    time (s)distance (m)10203040204060801001201401601802002200XY
    (a)

    Write down which of the two runners was running faster.

    (b)

    Find the speed of runner \(X\). Give your answer in metres per second.

    (c)

    How much further had runner \(X\) run than runner \(Y\) after \(40\) seconds?

    Show answer
    (a) Runner X
    (b) \(5\ \text{m/s}\)
    (c) \(120\ \text{m}\)
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  6. Either paper 2 marks

    Tomas's home is 800 metres from a shop.

    Tomas walked from home to the shop at a constant speed in 11 minutes. Tomas stayed at the shop for 5 minutes. Tomas walked home at a constant speed in 11 minutes.

    Tomas drew this distance-time graph to represent his journey.

    time (minutes)distance from home (m)5101520253035404520040060080010001200140016001800200022000

    Make two criticisms of his graph.

    Criticism 1 ......................................................

    Criticism 2 ......................................................

    Show answer
    Criticism 1: The stay at the shop is drawn going from 800 m to 1000 m, but it should be horizontal because nobody moves during a stay. Criticism 2: The walk home is drawn ending 1200 m from home, but it should end at home, 0 m from home.
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  7. Either paper 4 marks

    A tank contains \(40\) litres of water.

    Water leaks out of the tank at a rate of \(0.8\) litres per minute.

    The leak is stopped after \(20\) minutes.

    (a)

    Show that, when the leak is stopped, the tank contains \(24\) litres of water.

    (b)

    The tank is then refilled with water from a tap.

    The graph shows the volume of water in the tank after the leak is stopped.

    time since the leak stopped (minutes)volume of water in the tank (litres)24681012141648121620242832364044480

    Complete this report by writing a number in each answer space.

    The tap starts to refill the tank .......... minutes after the leak is stopped.

    (c)

    The rate at which the tank refills is .......... litres per minute.

    Show answer
    (a) \(0.8 \times 20 = 16\) litres leaked, and \(40 - 16 = 24\) litres left
    (b) \(7\ \text{minutes}\)
    (c) \(2.5\ \text{litres per minute}\)
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  8. Either paper 4 marks

    A taxi firm charges a fixed amount for every journey, plus an extra amount for each mile travelled.

    The graph shows the cost of a journey of up to \(16\) miles.

    distance (miles)cost (£)2468101214165101520253035400
    (a)

    Write down the amount the taxi firm charges before it has travelled any distance at all.

    (b)

    Find the gradient of the line.

    (c)

    Write down what the gradient tells you about the cost of a journey.

    Show answer
    (a) \(\text{£}5\)
    (b) \(2\)
    (c) The taxi firm charges £2 for each extra mile travelled.
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  9. Either paper 3 marks

    Reuben visits a library.

    He cycles to the library in 90 minutes at a speed of 9 miles per hour.

    He stays at the library for 20 minutes.

    He then cycles home.

    The sketch graph represents the visit.

    clock timedistance from home11:4514:21

    Work out the speed, in miles per hour, at which Reuben cycles home.

    Give your answer to 1 decimal place.

    Show answer
    \(17.6\ \text{mph}\)
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  10. Either paper 4 marks

    Rosa goes on a car journey from home.

    For the first 30 minutes her average speed is 30 miles per hour.

    Rosa then stops for 20 minutes.

    Rosa then completes the journey at an average speed of 30 miles per hour.

    The total journey time is 120 minutes.

    time (minutes)distance from home (miles)204060801001201020304050607080901001100
    (a)

    On the grid, draw a distance-time graph for Rosa's journey.

    Plot the point where the journey starts, each point where the graph changes direction and the point where the journey ends, then join them.

    (b)

    Write down the average speed for the whole journey.

    Show answer
    (a) Straight lines joining \((0, 0)\), \((30, 15)\), \((50, 15)\) and \((120, 50)\)
    (b) \(25\ \text{mph}\)
    (a)time (minutes)distance from home (miles)204060801001201020304050607080901001100
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discia.org Real Life and Distance Time Graphs · sheet 1
Answers Real Life and Distance Time Graphs · sheet 1
  1. (a) \(15\ \text{m}\)
    (b) \(3\ \text{m/s}\)
  2. (a) \(10\ \text{minutes}\)
    (b) \(16\ \text{km}\)
    (c) The van was not moving. It stayed 8 km from the depot while the delivery was made.
  3. (a) \(10\ \text{minutes}\)
    (b) \(45\ \text{km/h}\)
    (c) The outward journey
  4. (a) \(50\ \text{km}\)
    (b) \(100\ \text{km/h}\)
  5. (a) Runner X
    (b) \(5\ \text{m/s}\)
    (c) \(120\ \text{m}\)
  6. Criticism 1: The stay at the shop is drawn going from 800 m to 1000 m, but it should be horizontal because nobody moves during a stay. Criticism 2: The walk home is drawn ending 1200 m from home, but it should end at home, 0 m from home.
  7. (a) \(0.8 \times 20 = 16\) litres leaked, and \(40 - 16 = 24\) litres left
    (b) \(7\ \text{minutes}\)
    (c) \(2.5\ \text{litres per minute}\)
  8. (a) \(\text{£}5\)
    (b) \(2\)
    (c) The taxi firm charges £2 for each extra mile travelled.
  9. \(17.6\ \text{mph}\)
  10. (a) Straight lines joining \((0, 0)\), \((30, 15)\), \((50, 15)\) and \((120, 50)\)
    (b) \(25\ \text{mph}\)
    (a)time (minutes)distance from home (miles)204060801001201020304050607080901001100
discia.org Real Life and Distance Time Graphs · sheet 1