Question

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?

Answer 1

Plane Speed (x) = 378 mph

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