SOLUTION: A motorcycle is traveling at 70 mph over takes a car that is traveling at 30 mph, that had a 3 hour head start. How long will it take for the motorcycle to meet the car?

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Question 950718: A motorcycle is traveling at 70 mph over takes a car that is traveling at 30 mph, that had a 3 hour head start. How long will it take for the motorcycle to meet the car?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the head start of the car in miles
+d%5B1%5D+=+r%2At+
+d%5B1%5D+=+30%2A3+
+d%5B1%5D+=+90+ mi
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Start a stopwatch when the motorcycle leaves
Let +t+%7D%7C%7D%7D+=+time+in+hrs+on+stopwatch+when+%0D%0Athey+meet%0D%0ALet+%7B%7B%7B+d+ = distance in miles the motorcycle
travels until they meet
---------------------
The car's equation:
(1) +d+-+90+=+30t+
The motorcycle's equation:
(2) +d+=+70t+
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Substitute (2) into (1)
(1) +70t+-+90+=+30t+
(1) +40t+=+90+
(1) +t+=+2.25+ hrs
The motorcycle took 2 hrs and 15 min to
meet the car
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check:
(2) +d+=+70t+
(2) +d+=+70%2A2.25+
(2) +d+=+157.5+
and
(1) +d+-+90+=+30%2A2.25+
(1) +d+=+90+%2B+67.5+
(1) +d+=+157.5+
OK