college algebra word problem

Question

A plane traveling with the wind travels 700 miles in 5 hours. The return trip is against the wind and takes 7 hours. Find the rate of the plane in still air and the rate of the wind.

Answer 1

with the wind the speed was 700/5 = 140 mph

against the wind the speed was 700/7 = 100 mph

a rough guess would be the average (140+100)/2 = 120 mph

let r = the speed in still air and w= wind speed

d=st

distance = rate of speed times time:

700 = (r+w)5 = (r-w)7

that's 2 equations, 2 unknowns

700=(r+w)5 or

140 = r+w

and

700 = (r-w)7

100 = r-w

add the 2 last equations

to get 2r = 240

r = 120 mph for speed in still air

w = 20 mph

check the answers

d=st

700= (120+20)5 = 140(5) = 700

700= (120-20)7 = 100(7) = 700