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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
Work out Olly's average speed for his total drive from Liverpool to Sheffield.
Answer
To find Olly's average speed for the total journey, we first need to calculate the total distance and the total time taken.
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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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Total Time:
- Time taken from Liverpool to Manchester:
- Average Speed = 70 km/h
- Time = Distance / Speed = 56 km / 70 km/h = 0.8 hours = 48 minutes
- Time taken from Manchester to Sheffield = 75 minutes = 1.25 hours
- Total Time = 48 minutes + 75 minutes = 123 minutes = 2.05 hours
- Time taken from Liverpool to Manchester:
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Average Speed Calculation:
- Average Speed = Total Distance / Total Time
- Average Speed = 117 km / 2.05 hours ≈ 57.1 km/h
Thus, Olly's average speed for his total drive from Liverpool to Sheffield is approximately 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's approach of averaging the speeds (80 km/h and 60 km/h) is correct, it suggests that the time taken for both parts of the journey (from Barnsley to Leeds and from Leeds to York) must be taken into account. This means that:
- The distances covered between Barnsley to Leeds and Leeds to York are proportional to the speeds she mentioned.
- If Janie is averaging the speeds without accounting for the different distances, it implies that the distances from Barnsley to Leeds and Leeds to York should ideally be the same for the average speed to be valid.
Therefore, Janie’s assumption may only hold true if the distances for both parts of the journey are equal or if she adjusts her average calculation based on the actual distances.