Question

Correct

A plane travels at a speed of 170 mph in still air. Flying with a tailwind, the plane is clocked over a distance of 875 miles. Flying against a
headwind, it takes 2 hours longer to complete the return trip. What was the wind velocity? (Round your answer to the nearest tenth.)

Answer 1

To find the wind velocity, we can use the equation Ground Speed = Airspeed + Wind Speed. By setting up two equations using the time it takes to complete the trip with the tailwind and against the headwind, we can solve for the wind velocity. The wind velocity is approximately 22.4 mph.

Step-by-step explanation:

To find the wind velocity, we need to use the formula:

Ground Speed = Airspeed + Wind Speed

Let's assume that the wind speed is x mph. The plane's ground speed while flying with a tailwind would then be 170 + x mph. Given that it travels 875 miles with the tailwind, we can set up the equation:

Time = Distance / Speed

Time = 875 / (170 + x)

= 5 hours

For the return trip against the headwind, the plane's ground speed would be 170 - x mph. It takes 2 hours longer to complete the return trip, so the time would be:

Time = Distance / Speed

Time = 875 / (170 - x)

= 5 + 2

= 7 hours

Solving this equation, we can find the wind velocity (x) to be approximately 22.4 mph (rounded to the nearest tenth).