Problema Solution
The airspeed of a plane is its speed through the air. This speed contrasts with the plane's groundspeed its speed relative to the ground. The groundspeed of an air-plane is affected by the speed of the wind. Suppose that a Boeing 767 flying west from Washington D.C., to San Francisco, a distance of 2400 miles, takes 6 hours. The trip east from San Francisco to Washington D.C., takes 4 hours. Find the airspeed of the plane and the effect wind resistance has on the plane.
Answer provided by our tutors
let
a = the airspeed of the plane
w = the impact of wind resistance
d = 2400 mi the flight distance in one direction
going against the wind the planes speed is: a - w
since speed*time = distance we have
(a - w)*6 = 2400 divide both sides by 6
a - w = 400
going with the wind the planes speed is: a + w
(a + w)*4 = 2400 divide both sides by 4
a + w = 600
by solving the system of equations
a - w = 400
a + w = 600
we find
a = 500 mph
w = 100 mph
The airspeed of the plane is 500 miles per hour.
The impact of wind resistance on the plane is 100 miles per hour.