find the speed of the plane in still air?

Question

A plane flies 390 miles with the wind and 325 miles against the wind in the same length of time. If the speed of the wind is 10mph find the speed of the plane in still air?

Answer 1

r · t = d

t = d/t

 

s = speed in still air

 

s + 10 = speed with the wind

s - 10 = speed against the wind

 

t = 390/(s + 10)       with the wind

t = 325/(s - 10)        against the wind

 

390/(s + 10) = 325/(s - 10)

390(s - 10) = 325(s + 10)

390s - 3900 = 325s + 3250

65s = 7150

s = 110

 

The speed of the plane in still air is 110 mph.