Question

A jetliner can travel 1700 miles from Fargo to Phoenix, Arizona in four hours with a tailwind, but it takes three hours to travel 975 miles from Phoenix to Boise, Idaho into the same wind. Determine the wind speed and the airspeed of the plane.

Answer 1

By creating equations based on the given times and distances, we can solve for the airspeed and wind speed. The airspeed of the plane is 375 mph, and the wind speed is 50 mph.

Step-by-step explanation:

To determine the wind speed and the airspeed of the plane based on the flight times and distances provided, we can set up a system of equations. Let p represent the airspeed of the plane in still air and w represent the wind speed. The given information allows us to create two scenarios:

• With a tailwind, the plane's effective speed is p + w, and it travels 1700 miles in 4 hours.
• Against the wind, the plane's effective speed is p - w, and it travels 975 miles in 3 hours.

From the first scenario, we can write the equation: (p + w) = 1700/4.

From the second scenario, we can write the equation: (p - w) = 975/3.

Solving these equations simultaneously, we get the system:

1. p + w = 425
2. p - w = 325

Add the two equations to eliminate w:

2p = 750 → p = 375

Substitute p = 375 into the first equation to find w:

375 + w = 425 → w = 50

Therefore, the airspeed of the plane is 375 mph and the wind speed is 50 mph.