at a maximum speed, an airolane travels 1680 miles against the windin 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours. Let x br the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?

Plane Speed (x) = 378 mph

Step-by-step explanation:

Equation

d = r * t

Givens

With the wind

d = 1680 miles t = 4 hours r = x + y

Against the wind

d = 1680 t = 5 hours r = x - y

Equation

The distances are the same, so you can solve for x in terms of y and then deal with the actual distance.

(x + y) * 4 = (x - y) * 5 Remove the brackets on both sides

Solution

4x + 4y = 5x - 5y Subtract 4x from both sides 4y = - 4x + 5x - 5y Combine 4y = x - 5y Add 5y to both sides 5y + 4y = x x = 9y

Solution part 2

Now take one of the distance formulas and solve for x first then y.

(x - y) * 5 = 1680 Substitute 9y for x (9y - y) * 5 = 1680 Subtract on the left 8y * 5 = 1680 Multiply on the left 40y = 1680 Divide by 40 y = 1680/40 y = 42 That's the speed of the wind. (x - y) * 5 = 1680 Substitute the wind speed for y (x - 42) * 5 = 1680 Divide both sides by 5 (x - 42) = 1680 / 5 Do the division on the right (x - 42) = 336 Add 42 to both sides. x = 336 + 42 x = 378 mph Plane's speed