Question

A light private plane can fly 120 mph in still air. Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind. Find the rate of the wind.

If w represents the rate of the wind, which expression represents the time it takes the plane to travel the 640 miles with the wind?

A. 640/(120+w),
B. 640/w, or
C. 640/(120-w)

Answer 1

A.640/(120+w)
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Answer 2

Answer:

rate of the wind: 40 mph

The expression that represents the time it takes the plane to travel the 640 miles with the wind is:  640/(120 + w )

Step-by-step explanation:

The plane fly at 120 mph. Let's call w, the rate of the wind.

Against the wind the speed of plane will be = 120 - w

With the wind the speed of plane will be = 120 + w

Speed is defined as: speed = distance/time

Time required to travel 320 miles against the wind:

time =  320/(120 - w )

Time required to travel 640 miles with the wind:

time =  640/(120 + w )

Both times are equal, then:

320/(120 - w ) = 640/(120 + w )

(320/640)*(120 + w ) = 120 - w

60 + 0.5*w = 120 - w

1.5*w = 60

w = 60/1.5 = 40 mph