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A train travelled along a track in 110 minutes, correct to the nearest 5 minutes - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 3
Question 17
A train travelled along a track in 110 minutes, correct to the nearest 5 minutes. He assumes that the track has been measured correct to the nearest 10 km. (a) Coul... show full transcript
Worked Solution & Example Answer:A train travelled along a track in 110 minutes, correct to the nearest 5 minutes - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 3
Step 1
Could the average speed of the train have been greater than 160 km/h?
Answer
To determine the average speed of the train, we can use the formula for speed:
v = \frac{d}{t}$$ where: - $v$ is the average speed, - $d$ is the distance traveled, - $t$ is the time taken. From the information given: - Time, $t = 110$ minutes = $\frac{110}{60}$ hours = $\frac{11}{6}$ hours. - Assuming the longest possible distance for the given track measurement to the nearest 10 km: - If the track length is measured at its upper limit, the actual distance is $270 km + 5 km = 275 km$. - Therefore, the average speed can be calculated as:v = \frac{275 \text{ km}}{\frac{11}{6} \text{ hours}} = \frac{275 \times 6}{11} = 150 \text{ km/h}$$
Since is less than , we conclude that the average speed of the train could not have been greater than .
Step 2
Explain how this could affect your decision in part (a).
Answer
If the track was measured to the nearest 5 km, this gives a potential distance for the track of anywhere between:
- Lower limit:
- Upper limit:
Thus the average speed could be recalculated using these limits:
- Using the upper limit:
- Using the lower limit:
In conclusion, measuring the track to the nearest 5 km means the average speed of the train can indeed be below , depending on the actual distance traveled, reinforcing that the initial assumption made in part (a) is valid but based on incorrect data.