A homing device left its home to deliver a mesage on takeoff

A homing device left its home to deliver a mesage. on takeoff, the device encountered a tailwind of 15 mph and made the delivery in 5 minutes. The return trip into the wind took 10 minutes. How fast does the device fly in still air?

Solution

Let x be the rate of the device in still air.
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Downwind DATA:
time = 1/12 hr ; rate = x+15 mph ; distance = rt = (1/12)(x+15) miles
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Upwind DATA:
time = 1/6 hr ; rate = x-15 mph ; distance = rt = (1/6)(x-15) miles
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Equation:
distance = distance
(1/12)(x+15) = (1/6)(x-15)
Multiply both sides by 12 to get:
x+15 = 2x-30
x = 45 mph (speed of the device in still air)