Question

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?

Answer 1

Answer:

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.