Question 1051863
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Rowing with the current, a canoeist paddled 10 mi in 2 h. Against the current, the canoeist could paddle only 6 mi in the same amount of time. 

Find the rate of the canoest in calm water and the rate of the current.
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<pre>
Let u be the the canoe rate in still water, in mph.
Let v be the rate of the current.

Then your governing equations are 

{{{10/2}}} = u + v   (1)   (the rate paddling with the stream)
{{{6/2}}}  = u - v   (2)   (the rate paddling against the srteam)

Simplify:

u + v = 5,     (3)
u - v = 3.     (4)

To solve, add the equations (3) and (4). You will get

2u = 5 + 3  --->  2u = 8  --->  u = 4.

Thus you found the canoe rate in still water. It is 4 mph.

Then from (3) v = 5 - u = 5-4 = 1.

<U>Answer</U>.  the canoe rate in still water is 4 mph. The rate of the current is 1 mph.
</pre>

It is a typical Upstream and Downstream round trips word problem.

You can find similar fully solved similar problems on upstream and downstream round trips with detailed solutions in the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> 


Read them attentively and learn how to solve this type of problems once and for all.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the section "<U>Word problems</U>", the topic "<U>Travel and Distance problems</U>".