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Question

A plane flies 288 mi with the wind in 2 hr. The return trip takes 3 hr. What is the speed of the wind and the speed of the plane in still air?

Answer 1

distance=rate*time

 

288=(r+w)*2

288=(r-w)*3

divide both sides of the first equation by 2

144=r+w

divide both sides of the second equation by 3

96=r-w

144=r+w

add the two equations

240=2r

r=240/2

r=120 mph is the speed of the plane

144=120+w

w=144-120

w=24 mph is the speed of the wind

Answer 2

distance = rate*time

with wind: d = (r+w)*t 

288=(r+w)*2

against wind: d =(r-w)*t

288=(r-w)*3

 

We can set these equations equal to one another since they are both equal to 288

 

2(r+w)=3(r-w)

2r+2w=3r-3w

-r=-5w

r=5w

 

Plug r into the "with wind" equation:

288=2(5w+w)

144=6w

w=24

r=5*w=5*24=120

 

Check our answers by plugging them into the "against wind" equation:

288=3(r-w)

288=3(120-24)

288=288

 

Thus, the wind speed is 24 mph and the speed of the plane in still air is 120 mph