Airplane Math Question?

Question

I am having trouble with this problem: A plane flies 2400 miles in 6 hours, with a tailwind all the way. The return trip on the same route, now with a headwind, takes 8 hours. Assuming both remain constant, find the speed of the plane and the speed of the wind. Can someone please show me how to work the problem?

Answer 1

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Let S = speed of plane and W = speed of wind

Distance = effective speed x time

For the journey out

2400 = (S + W) x 6

or

S + W = 2400 / 6 = 400

or

S = 400 - W

For the journey back

2400 = (S - W) x 8

or

S - W = 2400 / 8 = 300

or

S = 300 + W

Therefore as the plane's air speed is the same

300 + W = 400 - W

or

2 * W = 100

or

W = 50

Therefore S = 300 + 50 = 400 - 50 = 350

The Wind speed is 50 MPH

The plane's air speed is 350 MPH

The ground speed on the first leg is 400 MPH

The ground speed on the return leg is 300 MPH