An airplane flying into a headwind travels 690 miles in 3 hours and 50 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
A)plane speed = 220 mph; wind speed = 25 mph
B)plane speed = 182 mph; wind speed = 194 mph
C)plane speed = 205 mph; wind speed = 25 mph
D)plane speed = 220 mph; wind speed = 212 mph
E)plane speed = 182 mph; wind speed = 25 mph

Question

Quizplus · Accepted Answer

Let the airspeed of the plane be $p$ and the speed of the wind be $w$.
From the first part of the problem, we know that $690 = \left(3+\frac{50}{60}\right)p - 3w$ (since the plane is flying into a headwind, the ground speed is slower). Simplifying, we get:
$$
690 = \frac{19}{6}p - 3w
$$
From the second part of the problem, we know that $690 = 3p + 3w$ (since the wind is now helping the plane and the ground speed is faster). Simplifying, we get:
$$
690 = 3(p + w)
$$
Solving the second equation for $w$, we get $w = \frac{690}{3} - p = 230 - p$. Substituting this into the first equation, we get:
$$
690 = \frac{19}{6}p - 3(230 - p)
$$
Simplifying and solving for $p$, we get $p = 205$. Substituting this back into $w = 230 - p$, we get $w = 25$. Therefore, the airspeed of the plane is 205 mph and the speed of the wind is 25 mph, which corresponds to choice (C).

An Airplane Flying into a Headwind Travels 690 Miles in 3