Question

Ricky flies a plane against a headwind for 3185 miles. The return trip with the wind took 16 hours less time. If the wind speed is 8 mph, how fast does Ricky fly the plane when there is no wind? He flies ________ mph.

a) 273 mph
b) 256 mph
c) 288 mph
d) 304 mph

Answer 1

Ricky flies the plane at a speed of 288 mph when there is no wind.

Step-by-step explanation:

To find Ricky's speed when there is no wind, we can use the concept of relative velocities. When flying against a headwind, the plane's speed relative to the air mass is decreased by the wind speed. Similarly, when flying with the wind, the plane's speed relative to the air mass is increased by the wind speed.

Let's denote Ricky's speed when there is no wind as V mph. When Ricky flies against the headwind, his effective speed is (V - 8) mph. And when he flies with the wind, his effective speed is (V + 8) mph.

We are given that the round trip with the wind takes 16 hours less time compared to the trip against the wind. This means that the time taken to fly against the headwind is 16 hours longer than the time taken to fly with the wind. Using the formula Speed = Distance / Time, we can set up the following equation:

3185 / (V - 8) = 3185 / (V + 8) + 16

Simplifying and solving this equation, we find that V = 288 mph. So, Ricky flies the plane at a speed of 288 mph when there is no wind.