SOLUTION: This is a Rational Word Problem but i think it still goes under this category. The word problem is: My dog, Pooba, likes to swim in the river. Pooba can swim 6 miles per hour in st

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: This is a Rational Word Problem but i think it still goes under this category. The word problem is: My dog, Pooba, likes to swim in the river. Pooba can swim 6 miles per hour in st      Log On

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Question 520167: This is a Rational Word Problem but i think it still goes under this category. The word problem is: My dog, Pooba, likes to swim in the river. Pooba can swim 6 miles per hour in still water. He can swim 6 miles upstream in the same time it takes to swim 18 miles downstream. What is the speed of the river's current? Please help me.
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = speed of current in mi/hr
Let s = dog's swimming speed in still water in mi/hr
Let t = dog's time swimming both upstream
and downstream in hours
given:
+s+=+6+
---------
Swimming upstream:
(1) +6+=+%28+s+-+c+%29%2At+
(1) +6+=+%28+6+-+c+%29%2At+
Swimming downstream:
(2) +18+=+%28+s+%2B+c+%29%2At+
(2) +18+=+%28+6+%2B+c+%29%2At+
---------------
(1) +6+=+6t+-+c%2At+
(2) +18+=+6t+%2B+c%2At+
Add the equations
+24+=+12t+
+t+=+2+
and, since
(1) +6+=+6t+-+c%2At+
(1) +6+=+6%2A2+-+2c+
(1) +2c+=+12+-+6+
(1) +2c+=+6+
(1) +c+=+3+
The speed of the current is 3 mi/hr
check answer:
(2) +18+=+%28+6+%2B+c+%29%2At+
(2) +18+=+%28+6+%2B+3+%29%2A2+
(2) +18+=+9%2A2+
(2) +18+=+18+
and
(1) +6+=+6t+-+c%2At+
(1) +6+=+6%2A2+-+3%2A2+
(1) +6+=+12+-+6+
(1) +6+=+6+
OK

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Distance equals rate times time, so you can also say that time equals distance divided by rate. Since the upstream trip is against the current, the upstream rate is the still water rate MINUS the current rate, and the downstream rate is the still water rate PLUS the current rate. Let represent the rate of the current and then the following two expressions are equal because the time for the upstream trip is the same as the time for the downstream trip.



Cross multiply and then solve for . Doesn't matter what the dog's name is either; the answer is the same.

John

My calculator said it, I believe it, that settles it
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