An airplane flying into a headwind travels 216 miles in 2 hours and 42 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 = 71 mph; wind speed = 83 mph
B) plane speed = 109 mph; wind speed = 14 mph
C) plane speed = 94 mph; wind speed = 14 mph
D) plane speed = 71 mph; wind speed = 14 mph
E) plane speed = 109 mph; wind speed = 101 mph

Question

Quizplus · Accepted Answer

Let's denote the airspeed of the plane as $p$ and the speed of the wind as $w$.

Using the formula $distance = rate \cdot time$, we have:

For the first leg of the trip (against the wind):
$$216 = (p-w)\left(\frac{2}{3}\right)$$

Simplifying this equation, we get:
$$p-w = 324/2 = 162$$

For the second leg of the trip (with the wind):
$$216 = (p+w)2$$

Simplifying this equation, we get:
$$p+w = 108$$

Now we have two equations with two variables. Adding them, we get:
$$2p = 270$$
$$p = 135$$

Substituting this value back into one of the equations, we get:
$$135+w = 108$$
$$w = -27$$

This is impossible since the wind speed cannot be negative. Therefore, we made a mistake while solving the equations.

To correct that, notice that in the first equation, we can write $2$ hours and $42$ minutes as $2+\frac{42}{60}=2.7$ hours. Using this value instead of $\frac{2}{3}$, we get:
$$216 = (p-w)(2.7)$$
$$p-w = 80$$

Adding this equation to the second equation, we get:
$$2p = 188$$
$$p = 94$$

Substituting this value into one of the equations, we get:
$$94+w = 108$$
$$w = 14$$

Therefore, the airspeed of the plane is 94 mph and the speed of the wind is 14 mph.

Hence, the correct answer is (C).

An Airplane Flying into a Headwind Travels 216 Miles in 2