Problema Solution
A plane flies 390 miles with the wind and 325 miles against the wind in the same length of time. If the speed of the wind is 10 miles per hour, find the speed of the plane in still air.
Answer provided by our tutors
Let
v = the speed of the plane in still air, v>0
w = 10 mph the speed of the wind
Traveling with the wind the speed of the plane is: v + w = v + 10
Traveling against the wind the speed of the plane is: v - w = v - 10
Since speed = distance/time follows time = distance/speed
The time of the flight with the wind is equal to the time of the flight against the wind:
390/(v + w) = 325/(v - w)
390/(v + 10) = 325/(v - 10)
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v = 110 mph
The speed of the plane in still air is 110 mph.