Question

At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours.
Let x the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?

Answer 1

Let x the maximum speed of the plane and y be the speed of the wind.

We know that:
1)Distance = speed x time
2) if the head wind is y, then the resulting speed is x-y (against the wind)
3) if the tail wind is y, then the resulting speed is x+y (with the wind)

1) and 2): 2400 = (x-y).(6) or 6x-6y = 2400

1) and 3): 2400 = (x+y).(5) or 5x+5y = 2400

Hence the system of 2 equation:

6x - 6y = 2400
5x + 5y = 2400.
Solving it gives  x = 440 mi/h and y = 40 mil/h
Then the speed of the plane with no wind is 440 km/h