Question

A plane traveled 5780 miles with the wind in 8.5 hours and 4590 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

A) Plane speed: 650 mph, Wind speed: 70 mph
B) Plane speed: 550 mph, Wind speed: 50 mph
C) Plane speed: 480 mph, Wind speed: 40 mph
D) Plane speed: 700 mph, Wind speed: 80 mph

Answer 1

By setting up two equations based on the distances traveled with and against the wind, we find that the plane's speed in still air is 610 mph and the wind's speed is 70 mph, which does not match any of the given options.

Step-by-step explanation:

To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations based on the information given. Let p be the speed of the plane in still air and w be the speed of the wind. When traveling with the wind, the plane's effective speed is p + w and against the wind, it is p - w.

Using the distances and times provided:

• With the wind: 5780 miles / 8.5 hours = p + w = 680 mph
• Against the wind: 4590 miles / 8.5 hours = p - w = 540 mph

We can now set up two equations:

1. p + w = 680
2. p - w = 540

Adding these two equations gives us 2p = 1220, so p = 610 mph. To find w, we substitute p into one of the original equations: 610 + w = 680, giving us w = 70 mph.

Therefore, the speed of the plane in still air is 610 mph, and the speed of the wind is 70 mph, which is not one of the options given, suggesting a potential error in the options or the question setup.