Question

a plane flies 300 miles in 7 hours flying against headwinds. on the way back the trip takes 6 hours with the same winds. assuming the planes total velocity is internal (speedometer) plus the velocity of the winds how fast are the winds blowing?

Answer 1

let the speed of wind be y and the speed of plane be x.

we have

distance = rate*time

with the wind, we have

6(x+y) = 300 or 6x + 6y = 300 ---------------(1)

against the wind

7(x-y) = 300 or 7x - 7y = 300 ----------------------(2)

from (1), we find y as

y = (300-6x)/6 ----------------(3)

eq (2) becomes then

7x - 7(300-6x)/6 = 300

or 7x - 350 + 7x = 300

or 14x = 650 , x = 650/14 = 46.43

eq (3) then becomes

y = (300-6*46.43)/6 = 3.57

thus the velocity of plane is   x = 46.43 mph

the velocity of wind is y = 3.57 mph