SOLUTION: Suppose Josh runs from Point A to Point B at a rate of 12 mph and walks back from Point B to Point A at a rate of 4 mph. If the total time it takes Josh to run and walk is 80 minut

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Question 962804: Suppose Josh runs from Point A to Point B at a rate of 12 mph and walks back from Point B to Point A at a rate of 4 mph. If the total time it takes Josh to run and walk is 80 minutes, how long does it take Josh to walk back from Point B to Point A?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Running from A to B:
+d+=+r%2At%5B1%5D+
(1) +d+=+12t%5B1%5D+
-------------------
Walking from B to A:
(2) +d+=+4t%5B2%5D+
-------------------
+t%5B1%5D+%2B+t%5B2%5D+=+80%2F60+ hrs
(3) +t%5B1%5D+%2B+t%5B2%5D+=+4%2F3+ hrs
( note that I converted minutes to hrs )
-----------------------------------
Set (1) and (2) equal to each other
+12t%5B1%5D+=+4t%5B2%5D+
+t%5B2%5D+=+3t%5B1%5D+
Substitute this into (3)
+t%5B1%5D+%2B+3t%5B1%5D+=+4%2F3+
+4t%5B1%5D+=+4%2F3+
+t%5B1%5D+=+1%2F3+
and
+t%5B2%5D+=+3t%5B1%5D+
+t%5B2%5D+=+3%2A%281%2F3%29+
+t%5B2%5D+=+1+
-------------------
Walking back from B to A takes
him 1 hr
------------
check:
(1) +d+=+12t%5B1%5D+
(1) +d+=+12%2A%281%2F3%29+
(1) +d+=+4+ mi
------------------
(2) +d+=+4t%5B2%5D+
(2) +d+=+4%2A1+
(2) +d+=+4+ mi
OK