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A train leaves San Diego at 1:00PM. A second train leaves the same city in the same direction at 4:00PM.
The second train travels 78mph faster than the first. If the second train overtakes the first at 6:00PM,
what is the speed of each of the two trains?
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Let "v" be the speed of the first train (in mph);
then the speed of the second train is (v+78) mph, according to the condition.
Now, the distance traveled by the first train till the overtaking moment was 5v miles, where 5 is/are 5 hours from 1:00 pm till 6:00 pm.
The distance traveled by the second train till the overtaking moment was 2*(v+78) miles, where 2 is/are 2 hours from 4:00 pm till 6:00 pm.
The distance is the same, which gives you an equality
5v = 2(v+78).
Simplify and solve for "v":
5v = 2v + 156 ----> 3v = 156 ----> v = = 52.
Answer. The speed of the first train was 52 mph. The speed of the second train was 52 + 78 = 130 mph.
Solved.