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 milest = 4 hoursr = x + y

Against the wind

d = 1680t = 5 hoursr = 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 sides4y = -4x + 5x - 5y                    Combine4y = x - 5y                               Add 5y to both sides                       5y + 4y = xx = 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 left8y * 5 = 1680                  Multiply on the left40y = 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 + 42x = 378 mph                    Plane's speed