SOLUTION: A Boeing 747 flies 2420 miles with the wind. In the same amount of time it can travel 2140 miles against the wind. The cruising speed is 507mph. What is the speed of the wind?

Question 1033091: A Boeing 747 flies 2420 miles with the wind. In the same amount of time it can travel 2140 miles against the wind. The cruising speed is 507mph. What is the speed of the wind?
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
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A Boeing 747 flies 2420 miles with the wind. In the same amount of time it can travel 2140 miles against the wind.
The cruising speed is 507mph. What is the speed of the wind?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let w be the speed of the wind, in mph.
Then the plane flies at the speed (507+w) mph with the wind, and
                     at the speed (570-w) against the wind.

The plane spend  =  hours flying with the wind, and 
                 =  hours flying against the wind.

According to the condition,  = , which gives an equation

 = .

Now solve it for w. First multiply both sides by the common denominator (507-w)*(507+w) and then simplify. You will get

2420*(507-w) = 2140*(507+w),

2420*507 - 2420w = 2140*507 + 2140w,

2420*507 - 2140*507 = 2140w + 2420w,

(2420-2140)*507 = 4560w,

w =  = 31.13.

Answer. The speed of the wind is 31.13 mph.

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