SOLUTION: A train leaves Boston at 1 PM a second train leaves the same city in the same direction at 5 PM the second train travels 36 mph faster than the first if the second train overtake

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Question 1019044: A train leaves Boston at 1 PM a second train leaves the same city in the same direction at 5 PM the second train travels 36 mph faster than the first if the second train overtakes the first at 10 pm what is the speed of each of the two trains.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
From 1 PM to 5 PM is 4 hrs
Let +s+ = 1st train's speed in mi/hr
+s+%2B+36+ = 2nd train's speed in mi/hr
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Find the 1st train's head start in miles
+d%5B1%5D+=+s%2A4+
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From 5 PM to 10 PM is 5 hrs
The start time for these equations is 5 PM
Let +d+ = distance in miles the 2nd train travels
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Equation for 1st train:
(1) +d+-+4s+=+s%2A5+
Equation for 2nd train:
(2) +d+=+%28+s+%2B+36+%29%2A5+
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Substitute (2) into (1)
(1) %28+s+%2B+36+%29%2A5+-+4s+=+s%2A5+
(1) +5s+%2B+180+-+4s+=+5s+
(1) +4s+=+180+
(1) +s+=+45+
and
+s+%2B+36+=+81+
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The 1st train's speed is 45 mi/hr
The 2nd train's speed is 81 mi/hr
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check:
(1) +d+-+4s+=+s%2A5+
(1) +d+-+4s+=+s%2A5+
(1) +d+=+9s+
(1) +d+=+9%2A45+
(1) +d+=+405+ mi
and
(2) +d+=+%28+s+%2B+36+%29%2A5+
(2) +d+=+%28+45+%2B+36+%29%2A5+
(2) +d+=+81%2A5+
(2) +d+=+405+ mi
OK