Algebra Word Problem

Question

A plane can travel at 132 Kilometers per hour in still air. Flying with the wind, the plane traveled twice the distance in five hours as it traveled against the wind in three hours. What was the speed of the wind?

Answer 1

132 kph in still air

with the wind the plane goes twice the distance in 5 hours as it goes against the wind in 3 hours

what is the wind speed?? call it "w"

use d=rt, distance = rate of speed times time, r=d/t, t = d/r

with the wind speed = 132+w

against the wind speed = 132-w

2d/5 =132+w

d/3 = 132-w

2d = 660 +5w

d = 396 -3w

2d = 792-6w

2d = 660 +5w

subtract

0 = 132 -11w

11w = 132

w = 132/11 = 12 kph = wind speed

with the wind plane speed = 132+12 = 144 kph

against the wind plane speed = 132-12 = 120 kph

with the wind in 5 hours it goes 5x144 = 720 km

against the wind in 3 hours it goes 3x120 =360 km

720 = twice 360