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. Downwind DATA: time = 1/12 hr ; rate = x+15 mph ; distance = rt = (1/12)(x+10) miles Upwind DATA: time = 1/6 hr ; rate = x-15 mph ; distance = rt = (1/6)(x-10) miles

Equation: 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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