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The scale diagram below shows two cities, P and Q - OCR - GCSE Maths - Question 5 - 2018 - Paper 1
Question 5
The scale diagram below shows two cities, P and Q. Scale: 1 cm represents 125 km A plane departs from P at 09 47 and arrives at Q at 12 07. (a) Work out the avera... show full transcript
Worked Solution & Example Answer:The scale diagram below shows two cities, P and Q - OCR - GCSE Maths - Question 5 - 2018 - Paper 1
Step 1
a) Work out the average speed, in kilometres per hour, of the plane.
Answer
To find the average speed, we first need to calculate the distance between P and Q as well as the time taken for the journey.
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Calculate the Distance: From the scale given, 1 cm represents 125 km. Measure the distance on the diagram in cm and convert it to km. For example, if the distance measured is 4 cm, then:
Distance = 4 cm * 125 km/cm = 500 km.
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Calculate the Time Taken: The plane departs at 09:47 and arrives at 12:07.
Time taken = (12:07 - 09:47) = 2 hours 20 minutes = 2 + 20/60 = 2.333 hours.
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Calculate the Average Speed: Use the formula:
Average Speed = (\text{Distance} / \text{Time} = 500 \text{ km} / 2.333 \text{ hours} ≈ 214.29 \text{ km/h}.)
Thus, the average speed of the plane is approximately 214 km/h.
Step 2
b) Give one reason why your answer may be inaccurate.
Answer
One reason why the calculated average speed may be inaccurate is that the actual flight path may not have been a straight line. Factors such as air traffic control directives, weather conditions, and diversions can affect the exact route taken by the plane, leading to discrepancies between the calculated and actual speed.