A man running at a constant speed of 5 metres per second takes 66 seconds to complete a particular distance. A horse completes the same distance running at a constant speed of 15 metres per second. Find the difference, in seconds, in the times taken by the man and by the horse to run this distance.

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A man running at a constant speed of 5 metres per second takes 66 seconds to complete a particular distance - OCR - GCSE Maths - Question 10 - 2019 - Paper 1

Question 10

A man running at a constant speed of 5 metres per second takes 66 seconds to complete a particular distance. A horse completes the same distance running at a constan... show full transcript

Worked Solution & Example Answer:A man running at a constant speed of 5 metres per second takes 66 seconds to complete a particular distance - OCR - GCSE Maths - Question 10 - 2019 - Paper 1

Step 1

Calculate the distance run by the man

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Answer

To find the distance, we can use the formula:

distance = speed \times time

The man's speed is 5 m/s, and he takes 66 seconds to finish. Therefore:

distance = 5 \, \text{m/s} \times 66 \, \text{s} = 330 \, \text{meters}

Step 2

Calculate the time taken by the horse to cover the same distance

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Answer

Now, we need to find the time taken by the horse, which runs at a speed of 15 m/s. Using the formula:

time = \frac{distance}{speed}

Substituting the values we get:

time = \frac{330 \, \text{meters}}{15 \, \text{m/s}} = 22 \, \text{seconds}

Step 3

Find the difference in time taken by the man and the horse

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Answer

The man took 66 seconds, while the horse took 22 seconds. The difference in time is:

difference = 66 \, \text{s} - 22 \, \text{s} = 44 \, \text{seconds}

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