Question

At maximum speed, an airplane travels

2100 miles against the wind in 6 hours.
Flying with the wind, the plane can
travel the same distance in 4 hours.
Let x be the maximum speed of the plane and y
be the speed of the wind. What is the speed of
the plane with no wind?
Enter the correct answer.
________

Answer 1

The speed of the plane with no wind is 437.5 mph, found by solving the system of equations formed by the plane's speed against the wind (x - y = 350) and with the wind (x + y = 525).

Step-by-step explanation:

To find the speed of the airplane with no wind, we use the equations for motion with and against the wind. When the airplane travels against the wind, it moves slower by the wind speed, and when it travels with the wind, it moves faster by the wind speed. Let's use x to represent the maximum speed of the plane in still air, and y for the speed of the wind.

For the trip against the wind:

• The plane travels 2100 miles in 6 hours, so its speed against the wind is 2100 miles / 6 hours = 350 mph.
• The speed against the wind is the plane's speed minus the wind speed: x - y.
• We have the equation x - y = 350.

For the trip with the wind:

• The plane travels the same distance in 4 hours, so its speed with the wind is 2100 miles / 4 hours = 525 mph.
• The speed with the wind is the plane's speed plus the wind speed: x + y.
• We have the equation x + y = 525.

By solving these two equations together, we can find the values of x and y:

1. Add the two equations: (x - y) + (x + y) = 350 + 525
2. Simplify to get: 2x = 875
3. Divide by 2 to find x = 437.5 mph, which is the speed of the plane in still air.