ALGEBRA ONE WORD PROBLEM NUMBER 4

Question

If a plane can travel 490 hours with the wind and 430 hours against the wind, find the speed of the wind and the speed of the plane in still air.

Answer 1

Call the speed of the plane p, and the speed of the wind w.

When the plane is flying with the wind, the total speed is: p + w = 490

When the plane is flying against the wind, the total speed is p - w = 430

We can add these two equations together to eliminate w:

(p + w = 490)

+ (p - w = 430)

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2p = 920 ==> p = 460 (speed of plane)

Then the speed of the plane is 460, and the speed of the wind is (using p+w=490 to solve for w):

w = 490 - p = 490 - 460 = 30 (speed of wind)

(The units can be whatever you need, assuming mph seems safe)