Question 1070600
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The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. he has a boat in mind, but he can only test in on a... show more he speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. he has a boat in mind, but he can only test in on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator's needs? 
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Let me reformulate the problem equivalently in more convenient terms.


<pre>
    The round trip of 22.5 miles upstream and the same distance downstream takes 9 hours.
    Find the speed of the boat in still water if the current rate is 6 mph.
</pre>

<U>Solution</U>


<pre>
Let u be the speed of the boat in still water.

Then  the speed of the boat traveling upstream   is (u-6) mph, 
while the speed             traveling downstream is (u+6) mph.

The "time" equation is

{{{22.5/(u-6) + 22.5/(u+6)}}} = 9.

Solve for u. For it, multiply both sides by 2*(u-6)*(u+6). You will get

45(u+6) + 45*(u-6) = {{{18*(u^2-36)}}},   --->

90u = {{{18u^2 - 648}}},

{{{18u^2 - 90u - 648}}} = 0   --->   

{{{u^2 - 5u - 36}}} = 0  --->  (u-9)*(u+4) = 0  --->   

The only positive root is u = 9.


<U>Answer</U>.  The speed of the boat in still water is 9 mph.

<U>Check</U>.   {{{22.5/(9+6) + 22.5/(9-6)}}} = 9 hours.   Correct !!
</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>".