A homing device left its home to deliver a message On takeof

A homing device left its home to deliver a message. On takeoff, device encountered a tallwind of 9 mph and made the delivery in 10 minutes. The return trip into the wind took 10 minutes. How fast could the device fly in stiff air? In stiff air, the device could fly mph.

Solution

Suppose speed in still air = Vs

Speed of wind = Vw

first trip when he was tailwind, distance traveled:

d = (Vs + Vw)*t1

given

Vs + Vw = 9 mph

t1 = 5 min

Now when he was against the wind, distance traveled is same, So

d = (Vs - Vw)*t2

9*5 = (Vs - Vw)*10

Vs - Vw = 4.5

Vs + Vw = 9

Solving both equation

2*Vs = 13.5

Vs = 6.75 mph

Vw = 2.25 mph