Question

A plane traveled 3355 miles with the wind in 5.5 hours and 2585 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

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Answer 1

• Speed of the plane in still air is 540 mph,
• Speed of the wind is 70 mph

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Let the speed of plane is x and speed of the wind is y.

The speed of the plane with the wind is x + y and speed of the plane against the wind is x - y.

Equation for speed:

• speed = distance / time

Since the same amount of time spent in both cases, we can set equations:

• x + y = 3355/5.5 ⇒ x + y = 610
• x - y = 2585/5.5 ⇒ x - y = 470

Add up the two equations and solve for x:

• x + y + x - y = 610 + 470
• 2x = 1080
• x = 540

Find y:

• 540 + y = 610
• y = 610 - 540
• y = 70