SOLUTION: A boat travels 50 miles downstream in the same time that it takes to go 30 miles upstream. The speed of the boat in still water is a constant 36 miles per hour. Then, in mph, the s

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Question 621317: A boat travels 50 miles downstream in the same time that it takes to go 30 miles upstream. The speed of the boat in still water is a constant 36 miles per hour. Then, in mph, the speed of the stream is
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the stream
Let +t+ = the time to go upstream and downstream
Going downstream:
(1) +50+=+%28+36+%2B+s+%29%2At+
Going upstream:
(2) +30+=+%28+36+-+s+%29%2At+
--------------------
(1) +50+=+36t+%2B+s%2At+
(2) +30+=+36t+-+s%2At+
Add the equations
+80+=+72t+
+t+=+80%2F72+
+t+=+10%2F9+ hrs
and
(1) +50+=+%28+36+%2B+s+%29%2A%2810%2F9%29+
(1) +9%2A50+=+10%2A%28+36+%2B+s+%29+
(1) +45+=+36+%2B+s+
(1) +s+=+9+
The speed of the stream is 9 mi/hr
check:
(2) +30+=+%28+36+-+s+%29%2At+
(2) +30+=+%28+36+-+9+%29%2A%2810%2F9%29+
(2) +30+=+27%2A%2810%2F9%29+
(2) +270+=+270+
OK