Question 1095948
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a boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. 
what is the speed of the boat in still water? What is the speed of the current?
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<pre>
Let u be the motorboat speed in still water and v be the current rate.


The effective speed going downstream is 

{{{Distance/Time}}} = {{{336/12}}} = 28 miles per hour.


It is the <U>SUM</U> of the motorboat speed in still water and the rate of the current. It gives you your first equation

u + v = 28.    (1)



The effective speed going upstream is 

{{{Distance/Time}}} = {{{336/14}}} = 24 miles per hour.


It is the <U>DIFFERENCE</U> of the motorboat speed in still water and the rate of the current. It gives you your second equation

u - v = 24.    (2)


Thus you have this system of two equations in 2 unknowns

u + v = 28,    (1)   and
u - v = 24.    (2)


Add the two equations. You will get

2u = 28 + 24 = 52  ====>  u = {{{52/2}}} = 26 mph.


So, you just found the speed of the motorboat in still water.  It is  26 mph.

Then from the equation (1) you get  v = 28 - 26 = 2 mph is the current rate.


<U>Answer</U>.  The speed of the motorboat in still water is  26 mph.

         The current rate is 2 km/h.
</pre>

Solved.



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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=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.