Question

Flying against the wind, an airplane travels 2,880 miles in 4 1/2 hours. Flying with the wind, the airplane can travel the same distance in 4 hours. Find the speed of the wind?

Answer 1

we use distance = velocity * time equation, d=v*t

when the airplane is traveling against the wind, equation is:
d = (v.airplane - v.wind)*t
2880 = (v.airplane - v.wind)*4.5

when the airplane is traveling with the wind, equation is:
d = (v.airplane + v.wind)*t
2880 = (v.airplane + v.wind)*4

we combine these two equations:
2880 = (v.airplane - v.wind)*4.5
2880 = (v.airplane + v.wind)*4 --> 2880 = 4*v.airplane + 4*v.wind ->
2880 - 4*v.wind = 4*v.airplane
insert it into first equation <-- v.airplane = 720 - v.wind
2880 = ((720 - v.wind) - v.wind)*4.5
2880 = (720 - 2*v.wind)*4.5
2880 = 3240 - 9*v.wind
2880 - 3240 = -9*v.wind
-360 = -9*v.wind
v.wind = 40 miles/h