math equations

Question

Flying against the jetstream, a jet travels 4320 miles in 4 hours. Flying with the jetstream, the same jet travels 9240 miles in 7 hours. What is the rate of the jet in still air and what is the rate of the jetstream?

Answer 1

4320 in 4 hours upwind

9240 in 7 hours downwind

distance = rate of speed times time

d= rt

4320 = (r-w)4

9240 = (r+w)7

where r= plane speed in still wind

and w= wind jet stream speed

2 equations, 2 unknowns

solve the system of equations

4320/4 = r-w

9240/7 = r+w

add them to eliminate one variable

1080 + 1320 = 2r

r = 2400/2 = 1200 mph = plane speed in still air

w = r -1080 = 1200-1080 = 120 mph = jet stream speed

w= 1320-1200 = 120 mph

120+1200 = 1320 for 7 hours = 1320(7) = 9240 miles

1200-120 = 1080 for 4 hours = 1080(4) = 4320 miles

Answer 2

4320 = 4(r - w), r is the speed of the plane, w of the wind

9240 = 7(r + w)

Can you solve the system and answer?