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