Question

A plane can fly 312 miles with the wind in 3 hours, while it takes the same plane 4 hours to fly the same distance against the wind. Find the speed of the plane in still air, and the speed of the wind.

Answer 1

The  speed on the plane is 104mph while that of the wind is 78mph

Speed and distances

The formula for calculating distance is expressed as:

Speed = Distance/Time

If the plane is flying with the wind;

3(r+ w) = 312

r + w = 104 ................... 1

If against the wind

4(r - w )= 312

r- w = 78 .................. 2

Add both equations

2r = 104  + 78

2r = 182

r = 91

Since r + w = 104

w = 104 - 91

w = 13

Speed on the plane  = r + w  = 91 + 13 = 104mi/hr

Speed on the wind = 91 - 13 = 78mi/hr

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