SOLUTION: The Cuyahoga river has current of 2 mph. Two boats start downstream at the same time with one boat 5 miles faster in still water than the other one. How long will it take for the b

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Question 509378: The Cuyahoga river has current of 2 mph. Two boats start downstream at the same time with one boat 5 miles faster in still water than the other one. How long will it take for the boats to be 25 miles apart if the slower boat can travel 12 miles upstream in 2 hours?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time for the boats to be +25+%7D%7D+mi+apart%0D%0Agiven%3A%0D%0A%7B%7B%7B+c+=+2+ mi/hr is the current
+s+ mi/hr = speed of slower boat in still water
+s+%2B+5+ mi/hr = speed of faster boat in still water
The slower boat going upstream:
+12+=+%28+s+-+2+%29%2A2+
+12+=+2s+-+4+
+2s+=+16+
+s+=+8+ mi/hr
---------------
Going downstream:
slower boat:
+d+=+%28+8+%2B+2%29%2At+
(1) +d+=+10t+
faster boat:
+d+%2B+25+=+%28+8+%2B+5+%2B+2+%29%2At+
(2) +d+%2B+25+=+15t+
Substitute (1) into (2)
(2) +10t+%2B+25+=+15t+
(2) +5t+=+25+
(2) +t+=+5+
In 5 hrs, the boats will be 25 mi apart
check answer:
(1) +d+=+10%2A5+
(1) +d+=+50+ mi
and
(2) +d+%2B+25+=+15t+
(2) +75+=+15t+
(2) +t+=+5+
OK