math problem need help

Question

An airplane flies 4680 miles into the wind for 18 hours. The return trip takes 13 hours. Find the speed of the airplane without a wind and the speed of the wind.

Answer 1

distance = rate of speed times time

d=rt

4680= 18(p-w) = 13(p+w)

w= speed of the wind

p = speed of the plane in still air

that's 2 equations, 2 unknowns with a unique solution

18p-18w = 4680 and

13p+13w = 4680

p-w = 4680/18 = 260

p+w = 4680/13 = 360

add

2p = 620

p = 310 mph for the plane in still air

w = 360-310 = 50 mph = wind speed

check the answers

18(310)-18(50) = 18(310-50) = 18(260)= 4680

13(310)+13(50) = 13(310+50) = 13(360) = 4680