# How to interpret a distance time graph. Working out the speed by calculating the gradient.

Example

John cycles from his home to the shops. The shops are situated 15 km from his home and he cycles at a constant speed. After John has completed all of his shopping he returns home cycling back at a constants speed. The graph below shows his journey to the shops and back.

a) Work out the speed John cycles to the shops.

b) How much time does John spend shopping?

c) Calculate the speed of his return journey.

d) If john sets out at 10:47am at what time does he get back home?

a) A represents the outward journey, as the distance from his home is increasing over time. Now to work out the speed of the outward journey you need to divide the distance by the time, since speed = distance ÷ time.

The distance to the shops is 15km and the time it takes to get there is 2 hours. So the speed of this part of the journey is :

15 ÷ 2

= 7.5 kmph

The speed can also be found by finding the gradient of the line segment. You can do this by dividing the vertical height by the horizontal distance.

b) The time at the shops is represented by the horizontal line at the top of the graph as his distance from his home is no longer increasing.

So the time he takes at the shops is from t =2 to t =4, so the time he spends shopping is 2 hours.

c) The downwards slope at the end of the graph represents his return journey. It takes him 30 minutes to cover the 15km.

Like part a) use speed = distance ÷ time. Also change 30 minutes into hours (30 mins = ½ hour) so your answer is in kmph instead of km/minute

= 15 ÷ 0.5

= 30 kmph.

d) Finding the time he gets back home is quite easy. The total time is 4 ½ hours. So:

10:47am + 4 ½ hours is 3:17 pm.

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