a homing device left its home to deliver a message. on takeoff, the device encountered a tailwind of 10mph 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?
Let x be
the rate of the device in still air.
time = 1/12 hr ; rate = x+15 mph ; distance = rt = (1/12)(x+10) miles
time = 1/6 hr ; rate = x-15 mph ; distance = rt = (1/6)(x-10) miles
distance = distance
(1/12)(x+10) = (1/6)(x-10)
Multiply both sides by 12 to get:
x+10 = 2x-30
x = 30 mph (speed of the device in still air)
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