Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour.

GCSE Edexcel Maths Direct & Inverse Proportion: Jessica runs for 15 minutes at a

Jessica runs for 15 minutes at an average speed of 6 miles per hour - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 3

Question 6

Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes t... show full transcript

Worked Solution & Example Answer:Jessica runs for 15 minutes at an average speed of 6 miles per hour - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 3

Step 1

Calculate the distance for the first part of Jessica's journey.

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Answer

To find the distance, we can use the formula:

$\text{Distance} = \text{Speed} \times \text{Time}$

For the first part:

Speed = 6 miles/hour
Time = 15 minutes = \frac{15}{60} \text{ hours} = 0.25 \text{ hours}

Thus, the distance Jessica runs is:

$D_1 = 6 \times 0.25 = 1.5 \text{ miles}$

Step 2

Calculate the distance for the second part of Jessica's journey.

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Answer

For the second part:

Speed = 9 miles/hour
Time = 40 minutes = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}

Thus, the distance Jessica runs is:

$D_2 = 9 \times \frac{2}{3} = 6 \text{ miles}$

Step 3

Combine the distances to find the total distance run by Jessica.

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Answer

The total distance (D) run by Jessica is:

$D = D_1 + D_2 = 1.5 + 6 = 7.5 \text{ miles}$

Step 4

Calculate Amy’s average speed.

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Answer

Using the total distance and the time taken by Amy:

Time = 45 minutes = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}

Amy's average speed (S) is given by:

$S = \frac{\text{Total Distance}}{\text{Time}} = \frac{7.5}{0.75} = 10 \text{ miles/hour}$

Jessica runs for 15 minutes at an average speed of 6 miles per hour - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 3

Worked Solution & Example Answer:Jessica runs for 15 minutes at an average speed of 6 miles per hour - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 3

Calculate the distance for the first part of Jessica's journey.

Calculate the distance for the second part of Jessica's journey.

Combine the distances to find the total distance run by Jessica.

Calculate Amy’s average speed.

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