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 Algebraic Proof: 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 7 - 2022 - Paper 3

Question 7

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 7 - 2022 - Paper 3

Step 1

Calculate the distance for the first part of Jessica's run

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Answer

To find the distance Jessica runs during the first part of her run, we use the formula:

ext{Distance} = ext{Speed} imes ext{Time}

For the first part:

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

Thus,

ext{Distance} = 6 \times 0.25 = 1.5 \text{ miles}

Step 2

Calculate the distance for the second part of Jessica's run

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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,

ext{Distance} = 9 \times \frac{2}{3} = 6 \text{ miles}

Step 3

Calculate total distance run by Jessica

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Answer

The total distance Jessica runs is the sum of both parts:

ext{Total Distance} = 1.5 + 6 = 7.5 \text{ miles}

Step 4

Calculate Amy's average speed

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Answer

Amy takes 45 minutes to run the same total distance of 7.5 miles:

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

Using the average speed formula:

ext{Average Speed} = \frac{ ext{Total Distance}}{ ext{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 7 - 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 7 - 2022 - Paper 3

Calculate the distance for the first part of Jessica's run

Calculate the distance for the second part of Jessica's run

Calculate total distance run by Jessica

Calculate Amy's average speed

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