Question 1074633
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<pre>
Let V be the speed of the stream (of the current), in km/h

Then   the speed of the boat traveling downstream is (9+v) km/h, 
while  the speed of the boat traveling upstream   is (9-v) km/h.

The time for traveling upstream is {{{72/(9-v)}}} hours,
while The time for traveling downstream is {{{72/(9+v)}}} hours.

Therefore, the time equation is 

{{{72/(9-v) + 72/(9+v)}}} = 18   (total time).


Divide both sides by 18 and multiply both sides by (9-v)*(9+v). You will get

4(9+v) + 4*(9-v) = {{{81- v^2}}},   or

{{{v^2}}} = 81 - 2*36 = 9.


Therefore, v = 3 km/h is the rate of the current.


<U>Answer</U>.  The rate of the current is 3 km/h.
</pre>


It is a typical and standard Upstream and Downstream round trip word problem.

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

in this site.


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>".