Question

An airplane flew 3 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2 hours. Find the speed of the plane in still air.

180 mph

200 mph

220 mph

240 mph

Answer 1

Since the trip is the same forward and backward, the distance, d, is fixed. In other words, the plane travels the same distance in one direction that it does in the other direction.

The distance that an object travels, x, is equal to its velocity times time:
\[d=vt\]

So, the velocity times time of the forward trip is equal to the velocity times time of the return trip. Lets let v = the speed of the airplane in still air.

Forward trip: d=vt=(v-40m/h)(3 h)
Return trip: d=vt=(v+40m/h)(2 h)

These two must be equal, so set them equal:
\[(v-40 m/h)(3h) = (v+40 m/h)(2h)\] and solve for v.

Answer 2

First we need to get the velocity of the the plan with head wind and then the velocity of the plan with tail wind.

This is kinda like a d = r*t problem

Let x = velocity in still air
(x -40) = velocity of plain with head wind
(x +40) = velocity of plain with tail wind
The plain went the same distance so distance = distance
Solve the equation below and x will be the speed of the plain in still air

(x - 40)3 = (x +40)2