SOLUTION: On a bike hike, George Rode his bike at a rate of 6 miles per hour. 1 hour later paul began the bike hike. He rode At a rate of 7 miles an hour. In how many hours did Paul catch up

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Question 1024242: On a bike hike, George Rode his bike at a rate of 6 miles per hour. 1 hour later paul began the bike hike. He rode At a rate of 7 miles an hour. In how many hours did Paul catch up George?
Show the work please

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What was George's head start in miles?
+d%5B1%5D+=+6%2A1+
+d%5B1%5D+=+6+ mi
----------------
Start a stop watch when Paul leaves.
Let +t+ = time in hrs on stop watch when
Paul catches George
Let +d+ = distance Paul travels until he
catches George
----------------
George's equation:
(1) +d+-+6+=+6t+
Paul's equation:
(2) +d+=+7t+
-----------------
Substitute (2) into (1)
(1) +7t+-+6+=+6t+
(1) +t+=+6+
Paul catches George in 6 hrs
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check answer:
(2) +d+=+7t+
(2) +d+=+7%2A6+
(2) +d+=+42+ mi
and
(1) +d+-+6+=+6t+
(1) +d+-+6+=+6%2A6+
(1) +d+-+6+=+36+
(1) +d+=+42+ mi
OK