SOLUTION: The speed of a stream is 5 mph. If a boat travels 94 miles downstream in the same time it takes to travel 47 miles upstream what is the speed of the boat in still water? Please ex

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Question 581626: The speed of a stream is 5 mph. If a boat travels 94 miles downstream in the same time it takes to travel 47 miles upstream what is the speed of the boat in still water?
Please explain step by step.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water
+s+%2B+5+ = speed of boat going downstream
+s+-+5+ = speed of boat going upstream
Let +t+ = time going both upstream and downstream
----------
Going downstream:
(1) +94+=+%28+s+%2B+5+%29%2At+
Going upstream:
(2) +47+=+%28+s+-+5+%29%2At+
-----------------
(1) +94+=+s%2At+%2B+5t+
(2) +47+=+s%2At+-+5t+
------------------
Subtract (2) from (1)
(1) +94+=+s%2At+%2B+5t+
(2) +-47+=+-s%2At+%2B+5t+
+47+=+10t+
+t+=4.7+ hrs
and
(1) +94+=+%28+s+%2B+5+%29%2A4.7+
(1) +94%2F4.7+=+s+%2B+5+
(1) +20+=+s+%2B+5+
(1) +s+=+15+
The speed in still water is 15 mi/hr
check answer:
(2) +47+=+%28+15+-+5+%29%2At+
(2) +47+=+10t+
(2) +t+=4.7+
OK