Chapter A.8, Problem 46AYU

To determine

To find: How far can it fly and return safely?

Answer to Problem 46AYU

$742.5$ mi the plane can fly out and return safely.

Explanation of Solution

Given:

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/h.

Calculation:

Effective ground speed.

$300-30=270 \text{mph}$ against the wind.

$300+30=330 \text{mph}$ with the wind.

Let $d=$ the one-way distance; write a time equation, $\text{time}=\frac{\text{distance}}{\text{speed}}$.

Out bound time $+$ return time $=$ 5 hrs.

Therefore $\frac{d}{270}+\frac{d}{330}=5$.

That is $330d+270d=445500$.

$d=742.5$ mi the plane can fly out and return safely.