An airplane takes hours to travel a distance of kilometers against the wind. The return trip takes hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?

Rate of plane in still air = P = W (t1 + t2) / (t1-t2)

Rate of wind in still air = W = P (t1 - t2) / (t1 + t2)

Explanation:

Assuming speed of plane are the same on both trips

Rate (D/t1) = (P-W) ... EQU 1 going from city a to b

Rate (D/t2) = (P + W) ... Equ2 going back to city a

Where t1 is not equal to t2

Where D=distance between two cities

P &W are the speed of plane and wind

t1 &t2 = time taken for travel

Equ 1 & equ 2 becomes

D = (P - W) t1 ... equ3

D = (P + W) t2 equa4

Equating equ 3 and 4

Pt1 - Wt1 = Pt2 + Wt2

P (t1 - t2) = W (t1 + t2)

Rate of plane in still air = P = W (t1 + t2) / (t1 - t2)

Rate of wind in still air = W = P (t1 - t2) / (t1 + t2)