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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 = = 42 mph.
Then u+12 = 54 mph.
The problem is solved.