Question

A plane flies 2300 mi with the wind. In the same amount of​ time, it can fly 2020 mi against the wind. The cruising speed​ (in still​ air) is 540 mph. Find the speed of the wind.

A) 30 mph
B) 70 mph
C) 40 mph
D) 90 mph

Answer 1

The speed of the wind is 40 mph.

Step-by-step explanation:

To find the speed of the wind, we need to set up a system of equations based on the given information. Let's assume the speed of the wind is 'w' mph. When flying with the wind, the plane's speed is the sum of its cruising speed and the speed of the wind, so we have:

Speed with the wind = 540 + w. Distance with the wind = 2300 mi.

When flying against the wind, the plane's speed is the difference between its cruising speed and the speed of the wind, so we have:

Speed against the wind = 540 - w. Distance against the wind = 2020 mi.

Since the plane takes the same amount of time in both scenarios, we can set up an equation:

Distance with the wind / Speed with the wind = Distance against the wind / Speed against the wind.

Substituting the given values, we get:

2300 / (540 + w) = 2020 / (540 - w).

Now, we can cross-multiply and solve for 'w'. After simplifying, we obtain:

w = 40 mph.