Question 1070505
.
A man takes 5 hours and 20 minutes to row 6 miles up a river and back. If he can row 3 miles downstream in the same time 
that he can row 1 mile upstream, find the rate at which he rows and the rate of the current.
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<pre>
Let u be the rate of the boat at still water and v be the current rate (in miles-per-hour).

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


Hence, you have these two equations for two unknowns

{{{6/(u+v) + 6/(u-v)}}} = {{{5}}} {{{1/3}}}      (1)   ("A man takes 5 hours and 20 minutes to row 6 miles up a river and back")

{{{3/(u+v)}}} = {{{1/(u-v)}}}           (2)   ("he can row 3 miles downstream in the same time that he can row 1 mile upstream")


Simplify equation (1) in this way:

{{{6/(u+v) + 6/(u-v)}}} = {{{16/3}}}      (1') 

and replace  {{{6/(u-v)}}}  in  (1')  by {{{18/(u+v)}}}, based on (2). You will get

{{{6/(u+v) + 18/(u+v)}}} = {{{16/3}}},    or

{{{24/(u+v)}}} = {{{16/3}}},   or   (u+v) = {{{(24*3)/16}}} = {{{9/2}}}. 


Then from (2)  u-v = {{{(u+v)/3}}} = {{{9/(2*3)}}} = {{{3/2}}}.


You have now this system for u and v:

u + v = {{{9/2}}},    (3)
u - v = {{{3/2}}}.    (4)

Add the two equations. You will get

2u = {{{9/2 + 3/2}}} = {{{12/2}}} = 6.   Hence,   u = {{{6/2}}} = 3 miles per hour.

Now from (3),  v = {{{9/2 - 3}}} = {{{3/2}}} = 1.5 miles per hour.


<U>Answer</U>.  The boat speed in still water is 3 miles per hour.

         The current speed is 1.5 miles per hour.
</pre>


You can find many 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>".