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Olly drove 56 km from Liverpool to Manchester - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 2
Question 4
Olly drove 56 km from Liverpool to Manchester. He then drove 61 km from Manchester to Sheffield. Olly's average speed from Liverpool to Manchester was 70 km/h. Olly... show full transcript
Worked Solution & Example Answer:Olly drove 56 km from Liverpool to Manchester - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 2
Step 1
Olly's average speed from Liverpool to Sheffield
Answer
To calculate Olly's average speed for the total journey, we first determine the total distance and the total time taken.
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Calculate Total Distance:
- Distance from Liverpool to Manchester = 56 km
- Distance from Manchester to Sheffield = 61 km
- Total Distance = 56 km + 61 km = 117 km
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Calculate Time Taken:
- Time taken from Liverpool to Manchester = Distance / Speed = 56 km / 70 km/h = 0.8 hours = 48 minutes.
- Time taken from Manchester to Sheffield = 75 minutes = 75/60 hours = 1.25 hours.
- Total Time = 0.8 hours + 1.25 hours = 2.05 hours.
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Calculate Average Speed:
- Average Speed = Total Distance / Total Time = 117 km / 2.05 hours ≈ 57.1 km/h.
Step 2
If Janie is correct, what does this tell you about the two parts of Janie's journey?
Answer
If Janie is suggesting that the average speed can be calculated from the mean of her speeds, this implies that the time taken for both parts of her journey must be equal.
In reality, the distances and timings for both segments are different. Therefore, the mean of 80 km/h and 60 km/h does not accurately represent the average speed from Barnsley to York because the distances from Barnsley to Leeds and from Leeds to York are not equivalent, affecting the overall average speed.