SOLUTION: One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist travelled 6 miles per hour faster, how long will it take t

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Question 1024657: One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist travelled 6 miles per hour faster, how long will it take the cyclist to catch up with the hiker?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The hiker had a head start of
+d%5B1%5D+=+3%2A1+
+d%5B1%5D+=+3+ mi
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Start a stop watch when the cyclist leaves
Let +t+ = the time in hrs on the stop watch
when the cyclist catches up with the hiker
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Let +d+ = distance cyclist traveled until
cyclist caught up with hiker
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Hiker's equation:
(1) +d+-+3+=+3t+
Cyclist's equation:
(2) +d+=+6t+
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Substitute (2) into (1)
(1) +6t+-+3+=+3t+
(1) +3t+=+3+
(1) +t+=+1+
The cyclist takes 1 hr to catch up with hiker
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check:
(2) +d+=+6t+
(2) +d+=+6%2A1+
(2) +d+=+6+
and
(1) +d+-+3+=+3t+
(1) +d+-+3+=+3%2A1+
(1) +d+-+3+=+3+
(1) +d+=+6+
OK