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.