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.)

Jhun Vert's picture

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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