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A plane travels at a speed of 213 miles per hour - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 1

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A plane travels at a speed of 213 miles per hour. (a) Work out an estimate for the number of seconds the plane takes to travel 1 mile. (b) Is your answer to part (... show full transcript

Worked Solution & Example Answer:A plane travels at a speed of 213 miles per hour - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 1

Step 1

Work out an estimate for the number of seconds the plane takes to travel 1 mile.

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Answer

To find the time taken to travel 1 mile at a speed of 213 miles per hour, we can use the formula:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Substituting the values for Distance and Speed:

Time=1 mile213 miles per hour\text{Time} = \frac{1 \text{ mile}}{213 \text{ miles per hour}}

To convert the speed from miles per hour to miles per second, we can divide by 3600 (the number of seconds in one hour):

213mileshour=2133600milesseconds213 \frac{\text{miles}}{\text{hour}} = \frac{213}{3600} \frac{\text{miles}}{\text{seconds}}

Calculating the time:

  • First, calculate the speed in miles per second: 21336000.05917 miles per second\frac{213}{3600} \approx 0.05917 \text{ miles per second}
  • Now, finding the time taken to cover 1 mile: Time=10.0591716.89 seconds\text{Time} = \frac{1}{0.05917} \approx 16.89 \text{ seconds}

Thus, the time taken to travel 1 mile is approximately 17 seconds.

Step 2

Is your answer to part (a) an underestimate or an overestimate? Give a reason for your answer.

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The answer from part (a) is an underestimate.

This is because the average speed of 213 miles per hour does not account for factors such as acceleration or deceleration during flight. Hence, in practice, the actual time taken might be slightly longer due to these conditions. Additionally, using estimates often rounds down, leading to a shorter calculated time.

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