An aeroplane flies 3500 km in the same time that a train takes to travel 600 km. If the areoplane flies at a speed of 50 km/h more than five times the speed of the train, what are the speeds of the train and the aeroplane?
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Define x:
Let the speed of the train be x
The speed of the aeroplane = 5x + 50
Express the time the train took in term of x:
Time = Distance ÷ Speed
Time = 600/x
Express the time the aeroplane took in term of x:
Time = Distance ÷ Speed
Time = 3500/(5x + 50)
Time = 700/(x + 10)
Solve x:
The time taken is the same
600/x = 700/(x + 10)
600(x + 10) = 700x
600x + 6000 = 700x
100x = 6000
x = 60
Find the speed of the train and the aeroplane:
Speed of the train = x = 60 km/h
Speed of the aeroplane = 5x + 50 = 5(60) + 50 = 350 km/h
Answer: The speed of the train is 60 km/h and the speed of the aeroplane is 350 km/h
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