Question

a round trip flight of 1037.5 miles takes 7 1/2 hours. The part of the flight with the wind takes 1 1/2 less than the other part of the trip. Find the speed of the plane in still air and the speed of the wind.

I have no idea how to do, can u give me a lead on this? Some help?

Answer 1

speed of plane without wind --- x mph
speed of wind ------------- y mph
time to fly into wind = 1037.5/(x-y)
time to fly with the wind = 1037.5/(x+y)

1037.5/(x-y) - 1037.5(x+y) = 1.5
1037.5/(x-y) + 1037.5(x+y) = 7.5
add them
2075/(x-y) = 9
9x - 9y = 2075 .... #1

how about subtracting them:
2075/(x+y) = 6
6x + 6y = 2075 ... #2

#1 times 2 ---> 18x - 18y = 4150
#2 times 3 ---> 18x + 18y = 6225
add them:
36x = 10375
x = appr 288.2
in #2 , y = appr 57.6 mph