Question

A plane flies 405 miles with the wind and315 miles against the wind in the same amount of time. If the speed of the wind is 20 mph find the speed of the plane in still air

Answer 1

Answer:

  160 mph

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  time = distance/speed

__

If p represents the plane's speed, then the speed with the wind is p+20 and the time to go 405 miles is ...

  405/(p+20)

The speed against the wind is p-20, and the time to go 315 miles is ...

  315/(p-20)

These two times are equal, so we have ...

  405/(p+20) = 315/(p-20)

  405(p-20) = 315(p+20) . . . . . . cross multiply

  90p = 6300 +8100 = 14400 . . . . add 8100 -315p

  p = 14400/90 = 160

The speed of the plane in still air is 160 mph.