Question 1101210
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<pre>
Let u be the speed of the tugboat in still water (in miles per hour).

Let v e the speed of the current.


Then the speed of the tugboat downstream is (u+v) miles per hour.

The speed of the tugboat upstream is (u-v)  miles per hour.


From the other side, the speed downstream is {{{24/2}}} = 12 mph.     (it is the formula D =R*T, written in the form  R = {{{D/T}}} )
                                                               (Here R is the rate moving downstream.)


                     The speed   upstream is {{{16/2}}} = 8 hours.    (Again, it is the formula D =R*T, written in the form  R = {{{D/T}}} )
                                                               (Here R is the rate moving upstream.)


So you have these two equations

u + v = 12,   (1)
u - v =  8.   (2).


Add the two equations. You will get

2u = 12+8 = 20  ====>  u = {{{20/2}}} = 10.


It is the speed of the tugboat in still water.


Now the speed of the current, from the equation (1), is v = 12-u = 12 - 10 = 2 mph.


<U>Answer</U>.  The speed of the tugboat in still water is 10 mph.

         The speed of the current is  2 mph.
</pre>

Solved.



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It is a typical and standard Upstream and Downstream 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=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems-solvable-by-quadratic-equations.lesson>Wind and Current problems solvable by quadratic equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Unpowered-raft-moving-downstream-along-a-river.lesson>Unpowered raft floating downstream along a river</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, &nbsp;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>", &nbsp;the topic "<U>Travel and Distance problems</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.