A plane flies 465 miles with the wind and 315 miles against the wind in the same length of time. If the speed of the wind is 25 mph, find the speed of the plane in still air.

Answer: the speed of the plane in still air is 130 mph

Step-by-step explanation:

Let x represent the speed of the plane in still air.

A plane flies 465 miles with the wind. If the speed of the wind is 25 mph, it means that the total speed at which the plane flew is

x + 25

Distance = speed * time

Time = distance/speed

The time it took the plane to fly 465 miles would be

465 / (x + 25)

The plane flew 315 miles against the wind in the same length of time. it means that the total speed at which the plane flew is

x - 25

The time it took the plane to fly 315 miles would be

315 / (x - 25)

Since the time is the same, then

465 / (x + 25) = 315 / (x - 25)

Cross multiplying, it becomes

465 (x - 25) = 315 (x + 25)

465x - 11625 = 315x = 7875

465x - 315x = 7875 + 11625

150x = 19500

x = 19500/150

x = 130