The time taken to complete a journey halves as the speed doubles. On the axes below, sketch a graph to show this relationship. It takes 40 minutes to fill a garden pond using water from 5 identical hose pipes. Assuming the rate of flow of water from each hose pipe is the same, work out how many minutes it would take to fill the same garden pond using 2 of these hose pipes.

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The time taken to complete a journey halves as the speed doubles - OCR - GCSE Maths - Question 4 - 2023 - Paper 6

Question 4

The time taken to complete a journey halves as the speed doubles. On the axes below, sketch a graph to show this relationship. It takes 40 minutes to fill a garden... show full transcript

Worked Solution & Example Answer:The time taken to complete a journey halves as the speed doubles - OCR - GCSE Maths - Question 4 - 2023 - Paper 6

Step 1

Sketch a graph to show the relationship

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Answer

To illustrate the relationship between time taken and speed, you should draw a curve that starts at the top left of the graph and decreases towards the right, indicating that as speed increases, time taken decreases. The curve should approach the axes but not touch them. This reflects the inverse relationship where doubling the speed halves the time taken.

Step 2

Work out how many minutes it would take to fill the same garden pond using 2 of these hose pipes.

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Answer

Using 5 hose pipes, it takes 40 minutes to fill the pond. The flow rate from each pipe is combined, so if we find the equivalent time for 1 hose pipe, we get:

1 pipe takes: $40 \text{ minutes} \times 5 = 200 \text{ minutes}$ .

Using 2 hose pipes will halve this time:

Time with 2 pipes: $\frac{200 \text{ minutes}}{2} = 100 \text{ minutes}$ .

Thus, it would take 100 minutes to fill the pond using 2 hose pipes.

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