SOLUTION: A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels faster 12 mph faster than the first. If the second

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Question 1025053: A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels faster 12 mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains?
Answer by ikleyn(52781) About Me  (Show Source):
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A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM.
The second train travels faster 12 mph faster than the first. If the second train overtakes the first at 10:00 PM,
what is the speed of each of the two trains?
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Answer.
1-st train speed = 42 mph.
2-nd train speed = 54 mph.

Solution 

Let u = first train' speed, in mph.
Then the second train' speed is u+12 mph, according to the condition.

The first train traveled 9 hours before the second train overtakes the first one.
During this time the first train covered the distance of 9*u miles.

The second train traveled 7 hours before overtakes the first one.
During this time the second train covered the distance of 7*(u+12) miles.

These distances are the same. It gives you an equation

9u = 7*(u+12),   or 

9u = 7u + 84  --->  2u = 84  --->  u = 84%2F2 = 42 mph.

Then u+12 = 54 mph.

The problem is solved.