A homing device left its home to deliver a message. On takeoff, the device encountered a tailwind of 14 mph and made the delivery in 5 minutes. The return trip into the wind took 10 minutes. How fast could the device fly in still air?

speed in still air is 42 mph

Explanation:

given data

tail wind speed = 14 mph

time t1 = 5 min = 5/60 hr = 1/12 hr

return time t2 = 10 min = 10 / 60 hr = 1/6 hr

to find out

how fast they fly

solution

we consider here speed in still air is x

then

speed in wind will be = x + 14

and against wind speed = x - 14

so

distance = speed * time ... 1

so in wind distance = (x + 14) * 1/12 ... 2

and against wind distance = (x - 14) * 1/6 ... 3

so from equation 2 and 3

(x + 14) * 1/12 = (x - 14) * 1/6

x = 42

so speed in still air is 42 mph