Distance-Time Graphs

Go up from 09:30 on the time axis to the graph, then across to the distance axis.

Start at 4 on the distance axis, go across to the graph, then down to the time axis.

When Sara is stopped, her distance from home does not change. Each small square across is 15 minutes.

The vertical axis shows distance from home. What happens to that distance when Jo is heading home?

Read the distance from home at the petrol station and at the airport. The question asks for the distance between them.

Each small square across is 15 minutes and each small square up is 1 km.

Part (a)

1. The greatest distance from home is the highest point of the graph.
2. It is 9 km.

Part (b)

1. The graph first reaches 9 km at the start of the top flat part.
2. Each small square across is 15 minutes. That is at 12:30.

Speed = distance ÷ time. Read the distance and the time for the first part of the graph.

1. Before the break Dev drove from 08:00 to 10:00, which is 2 hours.
2. In that time he went from 0 km to 140 km.
3. Speed =140\div2=70 km/h.

30 minutes is half an hour. How far would she go in a whole hour at the same speed?

1. In the first 30 minutes Lily cycled 9 km.
2. 30 minutes is half an hour, so in 1 hour she would cycle 9\times2=18 km.
3. Her speed was 18 km/h.

Compare how steep the parts are. Steepness downwards counts as well.

1. The steeper the line, the faster Max was cycling. A flat part means he had stopped.
2. Part C goes up 8 km in 30 minutes. Part A goes up 8 km in 1 hour and part D goes down 16 km in 2 hours.
3. Part C is the steepest, so he was cycling fastest on part C.

The graph shows distance from home, not distance from the park.

1. The park is 12 km from Nina's home.
2. At 15:30 the graph shows she was 8 km from home.
3. She had cycled 12-8=4 km from the park.

Each small square across is 5 minutes. Find when he left the shop, not when he got there.

1. Jake left the shop at the end of the flat part: 08:30.
2. He reached school at 08:55.
3. From 08:30 to 08:55 is 25 minutes.

Read the distance and the time for the part after the flat section. How many lots of 20 minutes are in an hour?

1. Omar left the service station at 13:00 and arrived at the hotel at 13:20: 20 minutes.
2. He drove from 20 miles to 36 miles: 16 miles.
3. 20 minutes is \frac{1}{3} of an hour, so his speed was 16\times3=48 miles per hour.

For (b), work out how long the journey home took using time = distance ÷ speed.

Part (a)

1. Hana reached the lake 60 minutes after leaving home.
2. She stayed 45 minutes, so she left at 60+45=105 minutes.

Part (b)

1. The lake is 15 km from home. At 12 km/h, 15 km takes 15\div12=1.25 hours.
2. 1.25 hours is 1 hour 15 minutes, which is 75 minutes.
3. She got home 105+75=180 minutes after leaving.

Add up the distance for every part of the journey where he was moving, going out and coming back.

1. Home to the sports centre: 10 km.
2. Sports centre back to the shop: 10-4=6 km.
3. Shop to home: 4 km. Total =10+6+4=20 km.

Use the total distance and the total time from leaving home to reaching the zoo.

1. The whole journey is 60 km.
2. It went from 13:00 to 15:30, which is 2.5 hours.
3. Average speed =60\div2.5=24 km/h.

They pass each other where their lines cross. Both lines show distance from village A, so read each person's line at the same time.

Part (a)

1. They passed each other where the two lines cross.
2. The lines cross at 6 km from A.

Part (b)

1. The lines cross halfway between 10:00 and 11:00.
2. They passed each other at 10:30.

Part (c)

1. At 11:00 Ruth was 8 km from A.
2. At 11:00 Sam had reached A, so he was 0 km from A.
3. They were 8-0=8 km apart.

Work out the total distance first, then the total time the whole journey took.

1. From the graph, the first part was 50 km in 60 minutes. The whole journey is 50+40=90 km.
2. At an average speed of 45 km/h, 90 km takes 90\div45=2 hours =120 minutes.
3. Driving time =60+45=105 minutes, so the break was 120-105=15 minutes.

Find how far is left after the cafe, and how long that takes at 80 km/h. Then work back from 13:30.

1. From the graph, Ewan reaches the cafe at 11:00, and the cafe is 50 km from home.
2. He has 110-50=60 km left. At 80 km/h this takes 60\div80=0.75 hours =45 minutes.
3. He must leave the cafe by 12:45. From 11:00 to 12:45 is 105 minutes.

Write each time in hours before you divide: 15 minutes is 0.25 of an hour.

1. To the castle: 30 km from 09:00 to 10:30, which is 1.5 hours. Speed =30\div1.5=20 km/h.
2. Home: 30 km from 12:00 to 13:15, which is 1.25 hours. Speed =30\div1.25=24 km/h.
3. 24-20=4 km/h faster on the way home.

For (a), use time = distance ÷ speed for the whole journey. For (b), read where and when the stop ends.

Part (a)

1. Time =210\div60=3.5 hours, which is 3 hours 30 minutes.
2. 08:30 plus 3 hours 30 minutes is 12:00.

Part (b)

1. After the stop the coach leaves at 10:30, 90 km from London.
2. It has 210-90=120 km to go, from 10:30 to 12:00: 1.5 hours.
3. Speed =120\div1.5=80 km/h.