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James and Peter cycled along the same 50 km route - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 1

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James and Peter cycled along the same 50 km route. James took 2 1/2 hours to cycle the 50 km. Peter started to cycle 5 minutes after James started to cycle. Pete... show full transcript

Worked Solution & Example Answer:James and Peter cycled along the same 50 km route - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 1

Step 1

Calculate James' speed

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Answer

To find James' speed, we use the formula:

ext{Speed} = rac{ ext{Distance}}{ ext{Time}}

James' distance is 50 km, and his time is 2.5 hours. Therefore,

ext{Speed of James} = rac{50 ext{ km}}{2.5 ext{ h}} = 20 ext{ km/h}

Step 2

Calculate the time taken by James to cycle 15 km

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Answer

Using the speed we calculated:

ext{Time} = rac{ ext{Distance}}{ ext{Speed}} = rac{15 ext{ km}}{20 ext{ km/h}} = 0.75 ext{ h} = 45 ext{ minutes}

Step 3

Calculate the time taken by Peter to cycle 15 km

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Answer

Since Peter starts cycling 5 minutes (or (\frac{1}{12}) hours) after James, the effective time for Peter to cycle is:

extTimePeter=45extmin+5extmin=50extmin=56exth ext{Time}_{Peter} = 45 ext{ min} + 5 ext{ min} = 50 ext{ min} = \frac{5}{6} ext{ h}

Step 4

Calculate Peter's speed

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Answer

Using the formula for speed again:

ext{Speed}_{Peter} = rac{ ext{Distance}}{ ext{Time}} = rac{15 ext{ km}}{\frac{5}{6} ext{ h}} = 15 ext{ km} \times \frac{6}{5} = 18 ext{ km/h}

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