# Range of an Airplane

An air rescue plane averages
300 miles per hour in still air. It carries enough fuel for 5
hours of flying time. If, upon takeoff, it encounters a head
wind of 30 mi/hr, how far can it fly and return safely?
(Assume that the wind remains constant.)

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### With the headwind or flying

With the headwind or flying against the wind, the net speed of flying is $v_\text{airplane} - v_\text{wind}$. And with the tailwind or flying with the wind, the net speed is $v_\text{airplane} + v_\text{wind}$. From $s = vt$, we will use $t = \dfrac{s}{v}$ to define the total time of 5 hours.

$t_\text{headwind} + t_\text{tailwind} = 5$

$\dfrac{d}{300 - 30} + \dfrac{d}{300 + 30} = 5$

$\dfrac{2d}{927} = 5$

$d = 742.5 \text{ miles}$

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