SOLUTION: Jim left Denver on a bicycle riding at 12 mph. Four hours later Sally left by car, driving at 52 mph over the same route. How long will it take Sally to overtake Jim?

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Question 1108737: Jim left Denver on a bicycle riding at 12 mph. Four hours later Sally left by car, driving at 52 mph over the same route. How long will it take Sally to overtake Jim?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Jim's headstart in miles is:
+d%5B1%5D+=+12%2A4+
+d%5B1%5D+=+48+
Start a stop watch when Sally leaves.
Let +t+ = time in hrs on stop watch when
Sally catches up with jim.
Let +d+ = distance in miles that Sally travels
during time +t+
-----------------------------------------------
Jim's equation:
(1) +d+-+d%5B1%5D+=+12t+
Sally's equation:
(2) +d+=+52t+
--------------------------
(1) +d+-+48+=+12t+
(1) +d+=+12t+%2B+48+
--------------------------
Plug (2) into (1)
(1) +52t+=+12t+%2B+48+
(1) +40t+=+48+
(1) +t+=+6%2F5+
------------------------
+6%2F5+=+1+%2B+1%2F5+ hrs
+%281%2F5%29%2A60+=+12+ min
It will take 1 hr and 12 min for Sally to overtake Jim
------------------------
check:
(2) +d+=+52%2A%286%2F5%29+
(2) +d+=+62.4+
and
(1) +d+-+48+=+12%2A%286%2F5%29+
(1) +d+=+48+%2B+14.4+
(1) +d+=+2.4+
OK