An airplane flying into a headwind travels 328 miles in 2 hours and 44 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
A)plane speed = 157 mph; wind speed = 29 mph
B)plane speed = 157 mph; wind speed = 22 mph
C)plane speed = 119 mph; wind speed = 11 mph
D)plane speed = 119 mph; wind speed = 22 mph
E)plane speed = 142 mph; wind speed = 22 mph

Question

Quizplus · Accepted Answer

To solve this, we first convert the time of 2 hours and 44 minutes into hours, which is 2.733 hours. Let $p$ be the plane's airspeed and $w$ be the wind speed. For the trip against the wind, the effective speed is $p - w$ and the equation is $328 = (p - w) \times 2.733$. For the return trip with the wind, the effective speed is $p + w$ and the equation is $328 = (p + w) \times 2$. Solving these two equations simultaneously gives $p = 142$ mph and $w = 22$ mph.

An Airplane Flying into a Headwind Travels 328 Miles in 2