SOLUTION: Two trains are 500 miles apart when they first start moving towards each other. If in two hours the distance between them is 300 miles and one train goes 20 miles faster than anot

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Question 1042458: Two trains are 500 miles apart when they first start moving towards each other. If in two hours the distance between them is 300 miles and one train goes 20 miles faster than another, find the speed of the faster train. (Note: there are two possible solutions. Find both.)
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Two trains are 500 miles apart when they first start moving towards each other. If in two hours the distance between them
is 300 miles and one train goes 20 miles faster than another, find the speed of the faster train.
(Note: there are two possible solutions. Find both.)
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Let "u" be the speed of the first (faster) train and "v" be the speed of the second train (in miles per hour).

The first equation is 

u + v = %28500-300%29%2F2   ( the distance between the train is decreased at the rate u + v, since they are moving toward each other ).

The second equation is 

u - v = 20.

Write both equations as a system:

u + v = 100,   (1)
u - v = 20.    (2)

To solve the system, add equations (1) and (2) (both sides). You will get

2u = 120.   Hence,  u = 120%2F2 = 60 mph.

Thus the first train speed is 60 mph.

Then the second train speed is v = 100 - v = 40 mph.

Answer.  60 mph and 40 mph.