at maximum speed, an airplane travels 1720 miles against th wind in 5 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 if the plane with no wind?

x = 387

Step-by-step explanation:

The wind acts in the opposite direction to the plane when the time is longer.

The wind acts in the same direction as the plane when the time is shorter.

Equation

d = r*t

Givens

d = 1720 x = plane's speed y = wind speed t1 = 5 hours t2 = 4 hours.

Substitution

d = (x + y) * t 1720 = (x + y) * 4 1720 = (x - y) * 5

Since the two distances are the same, you can equate the right hand sides.

(x + y) * 4 = (x - y) * 5 Remove the brackets. 4x + 4y = 5x - 5y Add 5y to both sides 4x + 4y + 5y = 5x - 5y + 5y Combine all the terms. 4x + 9y = 5x Subtract 4x from both sides 9y + 4x - 4x = 5x - 4x Combine 9y = x

Now use one of the given equations with the distance

1720 = (x + y) * 4 Substitute 9y for x 1720 = (9y + y) * 4 Combine 1720 = 10y * 4 Multiply the right 1720 = 40y Divide by 40 1720/40 = 40y/40 Do the division 43 = y y = wind speek 9y = x x = 9*y 9*43 = x x = 387 miles per hour.