KS3 Maths · Year 8 · Chapter 5: Applications of graphs · Lesson 2

Time graphs

Year 8About 60 minutesNo calculator46 marks

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Quick questions to start.

A1
Last lesson
Parking is £ $1.50$ for each hour or part of an hour. Find the cost of $2$ hours $10$ minutes.
[1 mark]
Answer
A2
Needed today
Write $2$ hours $15$ minutes in hours, as a decimal.
[1 mark]
Answer
A3
Needed today
A bus goes $30$ km in $45$ minutes at a steady speed. How far does it go in $15$ minutes?
[1 mark]
Answer
A4
From chapter 4
Find the median of $3$ , $8$ , $5$ , $11$ , $7$ .
[1 mark]
Answer

Example, then your turn

Year 8

Your teacher works through each example with you. Then try the one beside it.

Example 1

The graph shows three runners in a $1200$ m race. (a) Who ran at a steady speed? Give a reason. (b) Who was in the lead after $2$ minutes? (c) Who won, and by how many seconds?

Hint A straight line means the same distance every minute. The higher graph at a time is the one in front. Each runner finishes where the graph reaches

1200

B1
The graph shows two swimmers in a $400$ m race. (a) Who swam at a steady speed? (b) At what time did Dan overtake Eve? (c) Who won, and by how many seconds?
[4 marks]

Example 2

The graph shows the temperature of some soup as it is heated. (a) Estimate the temperature after $3$ minutes. (b) How long does it take the soup to reach $80^{\circ}$ C? (c) By how much does the temperature rise in the first $3$ minutes?

Hint To read a temperature, go up from the time to the curve, then across. To read a time, go across from the temperature to the curve, then down.

B2
A ball is thrown up into the air. The graph shows its height. (a) Write down the greatest height the ball reaches. (b) Write down the two times when the ball is $15$ m above the ground.
[3 marks]

Example 3

A coach travels at a steady speed of $80$ km/h for $3$ hours. (a) Make a table of the distance it has travelled after $0$ , $1$ , $2$ and $3$ hours. (b) Draw a distance–time graph. (c) Use your graph to find how far the coach travels in $1 \frac{1}{2}$ hours, and how long it takes to travel $200$ km.

Hint At a steady speed the distance goes up by

80

km every hour, so the graph is a straight line from

(0, 0)

B3
A cyclist rides at a steady speed of $12$ km/h for $4$ hours. (a) Draw a distance–time graph on the grid. (b) Use your graph to find how far she rides in $2 \frac{1}{2}$ hours. (c) Use your graph to find how long it takes her to ride $42$ km.
[4 marks]

Practice

Year 8

C1
Each graph has time across the bottom. Match each situation to a graph. A: the depth of water in a bath filled by a tap at a steady rate. B: the distance travelled by a car that speeds up as it pulls away from traffic lights. C: the height of a sunflower that grows quickly at first and then more slowly.
[3 marks]
AnswerA: $\dots$ B: $\dots$ C: $\dots$
C2
The graph shows the depth of water in Sam's bath. He gets in, and later gets out. Then he pulls out the plug. How long was Sam in the bath, and how long did the bath take to empty?
[3 marks]

C3
Water drips into a bucket at a steady rate. After $4$ minutes the water is $6$ cm deep. How deep is it after $10$ minutes? After how many minutes is it $21$ cm deep?
[3 marks]

Exam-style questions

GCSE Foundation

D1
Jo says, "On a distance–time graph, a flat line shows someone travelling at a steady speed."
Is Jo correct? Give a reason for your answer.
[2 marks]

D2
Leon cycles from home. The distance–time graph shows his journey.
(a)
How far from home was Leon at 10:00?
[1 mark]
Answer $\dots$ km
(b)
Leon stopped twice. Work out the total time he was stopped.
[2 marks]
Answer $\dots$ hours
(c)
Work out Leon's speed on his way home. Give your answer in km/h.
[2 marks]
Answer $\dots$ km/h
(d)
Was Leon cycling faster before his first stop or after it? Give a reason for your answer.
[2 marks]
Total for D2: 7 marks
D3
The graph shows the temperature of an oven.
(a)
Write down the time when the oven was switched off.
[1 mark]
Answer $\dots$ minutes
(b)
For how long was the oven at a temperature of $150^{\circ}$ C or more?
[3 marks]
Answer $\dots$ minutes
Total for D3: 4 marks
D4
Water in a kettle is at $20^{\circ}$ C. The kettle is switched on. The water heats at a steady rate and reaches $100^{\circ}$ C after $4$ minutes.
(a)
Draw a graph on the grid to show the temperature of the water for the $4$ minutes.
[2 marks]
(b)
Use your graph to find the temperature after $1 \frac{1}{2}$ minutes.
[1 mark]
Answer $\dots^{\circ}$ C
(c)
Use your graph to find when the water reaches $65^{\circ}$ C. Give your answer in minutes and seconds.
[2 marks]
Answer $\dots$ min $\dots$ s
Total for D4: 5 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
The empty tank is made of two cuboids. Water flows in at $4$ litres a minute ( $1$ litre $= 1000$ cm³). How long does it take for the water to be $10$ cm deep, and how long to be $30$ cm deep? Which part of the depth–time graph is steeper? Give a reason.
[4 marks]
Not drawn accurately
Hint 1 · What to try
Work out how many minutes it takes to fill each part of the tank: volume $=$ base area $\times$ height.
Hint 2 · The first line
The bottom part holds $2000 \times 20 = 40000$ cm³, so it takes $40000 \div 4000 = 10$ minutes, and $10$ cm deep takes $5$ minutes.
Hint 3 · The full method
The top part holds $500 \times 20 = 10000$ cm³, which takes $2.5$ minutes. So $30$ cm deep is $10$ cm into the top part: $10 + 1.25 = 11.25$ minutes. The top part is steeper, because the water rises faster when the tank is narrower.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can read values from a time graph, forwards and backwards.
I can draw a distance–time graph for a steady speed.
I can describe a journey or a story from the shape of a graph.
I can work out a speed or a length of time from a graph.

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