SOLUTION: At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charle

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Question 644082: At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charleston headed for Washington, D.C., traveling at 50 mph. How long after the train leaves Charleston will the two trains pass each other?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 60 mi/hr train has a 1 hr head start
+d%5B1%5D+=+60%2A1+
The head start is +d%5B1%5D+=+60+ mi
Let +d+ = distance that 60 mi/hr train travels
after stopwatch starts until they meet
Let +t+ = time in hrs on stopwatch after
50 mi/hr train leaves
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Start a stop watch when the 50 mi/hr train leaves.
They both will now travel for the same amount
of time.
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60 mi/hr train's equation:
(1) +d+=+60t+
50 mi/hr train's equation:
(2) +500+-+%28+d+%2B+60+%29+=+50t+
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Substitute (1) into (2)
(2) +500+-+%28+60t+%2B+60+%29+=+50t+
(2) +500+-+60t+-+60+=+50t+
(2) +110t+=+440+
(2) +t+=+4+
4 hours after the 50 mi/hr train leaves Charleston
they will meet
check:
(1) +d+=+60%2A4+
(1) +d+=+240+
and
(2) +500+-+%28+d+%2B+60+%29+=+50%2A4+
(2) +500+-+d+-+60+=+200+
(2) +d+=+500+-+60+-+200+
(2) +d+=+240+
Note that 240 + 200 + 60 = 500 as it should