Question

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?

Answer 1

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