Problema Solution
a small plane flew 1056 miles in 4 hours with the wind. Then on the return trip, flying against the wind, the plane traveled 680 miles in 4 hours. What were the wind velocity and the speed of the plane?
Answer provided by our tutors
let
w = the wind speed
v = the speed of the plane in still air
d1 = 1056 mi
t1 = 4 h
d2 = 680 mi
t2 = 4 h
the speed of the plane with the wind is: v + w
the speed of the plane against the wind is: v - w
since speed=distance/time => distance = speed*time
with the wind
(v + w)t1 = d1
(v + w)4 = 1056 divide both sides by 4
v + w = 264
against the wind:
(v - w)t2 = d2
(v - w)*4 = 680 divide both sides by 4
v - w = 170
by solving the system of equations
v + w = 264
v - w = 170
we find
v = 217 mph
w = 47 mph
click here to see the step by step solution of the system of equations
the wind velocity is 47 miles per hour.
the speed of the plane is 217 miles per hour.