Problema Solution
A plane flew 715 miles in 2 hours and 10 minutes. The return trip took only 1 hour and 50 minutes. what was the speed of the wind? What was the speed of the plane in still air?
Answer provided by our tutors
let
x = spped of the wind
v = speed of the plane in still air
d = 715 miles the distance
t1 = 2 hours 10 min = 2 10/60 hours = 13/6 hours the time of the trip
t2 = 1 hour 50 min = 1 50/60 = 11/6 hours the time of the return trip
since t2 < t1 in the return trip the plane is flying in the direction of the wind while at the beginning it was flying against the speed of the wind:
the speed of the plane against the wind is v - x = 715 / (13/6) miles per hour
the speed of the plane in the return trip is v + x = 715 / (11/6) miles per hour
thus we can write
v - x = 715/(13/6)
v + x = 715/(11/6)
by solving the system of equations
v - x = 330
v + x = 390
we find
v = 360 mph
x = 30 mph
the speed of the plane in still air is 360 mph.
the speed of the wind is 30 mph.