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
