SOLUTION: Janet set off on a bicycle trip at 6:00 am at an average rate of 22 miles per hour. Her husband, Bob, promised to bring her some lunch, and he set off by car 2 hours after Janet l

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Question 1099950: Janet set off on a bicycle trip at 6:00 am at an average rate of 22 miles per hour. Her husband, Bob, promised to bring her some lunch, and he set off by car 2 hours after Janet left, driving at an average speed of 50 miles per hour. At what time did Bob catch up with Janet?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find Janet's head start in miles
+d%5B1%5D+=+22%2A2+
+d%5B1%5D+=+44+ mi
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Start a stopwatch when Bob leaves at 8:00
Let +t+ = time in hrs on the stopwatch
when Bob catches up with Janet
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Let +d+ = distance in miles that Bob travels
until he catches up with Janet
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Janet's equation:
(1) +d+-+d%5B1%5D+=+22t+
(1) +d+-+44+=+22t+
Bob's equation:
(2) +d+=+50t+
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Plug (2) into (1)
(1) +50t+-+44+=+22t+
(1) +28t+=+44+
(1) +t+=+1.5714+
and
+.5714%2A60+=+34.2857+
+.2857%2A60+=+17+
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+8+%2B+1+=+9+
Bob catches up at 9:34:17
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check:
(1) +d+-+44+=+22t+
(1) +d+=+22%2A1.5714+%2B+44+
(1) +d+=+34.5708+%2B+44+
(1) +d+=+78.5708+
and
(2) +d+=+50t+
(2) +d+=+50%2A1.5714+
(2) +d+=+78.57+
Close enough
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