Problema Solution

The airspeed of a plane is its speed through the air. The groundspeed of a plane is its speed relative to the ground. The groundspeed of an airplane is affected by the speed of the wind. Suppose that a plane flying 1800 miles west requires 12 hours and flying 1800 miles east requires 9 hours. Find the airspeed of the plane and the effect wind resistance has on the plane.

Airspeed of plane=____ mph

Speed of wind=____ mph

Answer provided by our tutors

distance = speed * time


let 'w' represent the speed effect of wind resistance in mph and 'v' represent the speed of the plane with no wind resistance, then 'v-w' represents the speed of the plane into the wind and 'v+w' represents the speed of the plane with the wind


the same distance is flown but flying west requires more time, therefore the westbound speed is 'v-w', into the wind, and the eastbound speed is 'v+w', with the wind


we have these equations:

1800 = 12(v-w) = 12v - 12w

1800 = 9(v+w) = 9v + 9w

solving this system we have:

v = 175

w = 25


the airspeed of the plane is 175 mph, the wind effect is 25 mph