Question 1068609
.
A paddle boat can move at a speed of 8 km/h in still water. The boat is paddled 4 km downstream in a river in the same time 
it takes to go 2 km upstream. What is the speed of the river?
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<pre>
Let "v" be the speed of the river (or, better to say, current rate), in km/h.

Then the speed of the boat downstream is (8+v) km/h (relative to the river banks),

and  the speed of the boat downstream is (8-v) km/h.


Therefore, the time for traveling 4 km downstream is {{{4/(8+v)}}} hours,

and        the time for traveling 2 km   upstream is {{{2/(8-v)}}} hours.


According to the condition, time {{{4/(8+v)}}} is the same as time {{{2/(8-v)}}}, which gives you an equation

{{{4/(8+v)}}} = {{{2/(8-v)}}}.    (1)


It is your equation to find the unknown "v". To solve it, multiply both sides of (1) by (8+v)*(8-v). You will get

4*(8-v) = 2*(8+v).


Simplify and solve for v:

32 - 4v = 16 + 2v  --->  32 - 16 = 2v + 4v  --->  6v = 16  --->  v = {{{16/6}}} = {{{8/3}}} km/h.

<U>Answer</U>.  The current rate is {{{8/3}}} km/h = {{{2}}}{{{2/3}}} km/h.

<U>Check</U>.  Speed downstream is {{{8+ 8/3}}} = {{{(24+8)/3}}} = {{{32/3}}} km/h;  Time downstream is {{{4/((32/3))}}} = {{{(4*3)/32}}} = {{{12/32}}} = {{{3/8}}} of an hour.

        Speed   upstream is {{{8- 8/3}}} = {{{(24-8)/3}}} = {{{16/3}}} km/h;  Time   upstream is {{{2/((16/3))}}} = {{{(2*3)/16}}} = {{{6/16}}} = {{{3/8}}} of an hour. 
</pre>

Solved and checked.


It is a typical and standard Upstream and Downstream trip word problem.

You can find many similar fully solved problems on upstream and downstream 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>".