Question 1059114
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A boat moves 7 kilometers upstream in the same amount of time it moves 20 kilometers downstream. 
If the rate of the current is 5 kilometers per hour, find the rate of the boat in still water.
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<pre>
Let "u" be the rate of the boat in still water, in {{{km/h}}}.

Then your governing equation ("time equation") is

{{{7/(u-5)}}} = {{{20/(u+5)}}}.

The left side is the time to travel 7 kilometers upstream.

The right side is the time to travel 20 kilometers downstream.

To solve the equation, multiply both sides by (u-5)*(u+5). You will get


7(u+5) = 20(u-5),  or

7u + 35 = 20u - 100,  or

35 + 100 = 20u - 7u,  or

135 = 13u  --->  u = {{{135/13}}}.


<U>Answer</U>. The rate of the boat in still water is  {{{135/13}}} {{{km/h}}}.

        Unfortunately, the person who invented these input numbers, select them too curve to get an integer number as the answer.
        Perhaps, this person didn't solve the problem himself.
</pre>

It is a typical "upstream and downstream Travel and Distance" word problem.


See 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> 

in this site.


You will find the detailed solutions of many similar problems there. 


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>".



If after reading my solution you still have a question "why the governing equation has this form ?", 
then read the lessons above. They contain the detailed answer to this question.