SOLUTION: Nancy can travel 8 miles upstream in the same time it takes her to go 12 miles downstream. Her boat goes 15 mph in still water. What is the rate of the current? Thanks in advance

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Question 955155: Nancy can travel 8 miles upstream in the same time it takes her to go 12 miles downstream. Her boat goes 15 mph in still water. What is the rate of the current?
Thanks in advance!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the rate of the current
+15+-+c+ = speed of boat going upstream
+15+%2B+c+ = speed of boat going downstream
+t+ = time in hours
--------------------
Going upstream:
(1) +8+=+%28+15+-+c+%29%2At+
Going downstream:
(2) +12+=+%28+15+%2B+c+%29%2At+
-----------------------
(1) +8+=+15t+-+c%2At+
(2) +12+=+15t+%2B+c%2At+
---------------------
Add the equations
+20+=+30t+
+t+=+2%2F3+ hrs
------------------
(1) +8+=+%28+15+-+c+%29%2A%282%2F3%29+
(1) +%283%2F2%29%2A8+=+15+-+c+
(1) +12+=+15+-+c+
(1) +c+=+3+
The rate of the current is 3 mi/hr
-----------
check:
(2) +12+=+%28+15+%2B+c+%29%2At+
(2) +12+=+%28+15+%2B+3+%29%2A%282%2F3%29+
(2) +12+=+18%2A%282%2F3%29+
(2) +12+=+12+
OK