Question 1045968
.
A paddle-boat can move at a speed of 6 km/h in still water. The boat is paddled 
16 km downstream in a river in the same time 
it takes to go 8 km upstream. What is the speed of the river? please show work
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<pre>
Let "u" be the speed of the river.
Then the speed of the paddle-boat floating downstream is 6 +u km/h.
and  the speed of the paddle-boat floating upstream   is 6 -u km/h.

Time it spends for floating 16 km downstream is {{{16/(6+u)}}} hours.
Time it spends for floating  8 km upstream   is {{{8/(6-u)}}} hours.

These times are equal, so you have an equation

{{{16/(6+u)}}} = {{{8/(6-u)}}}.

To solve it, multiply both sides by (6+u)*(6-u). You will get

16(6-u) = 8(6+u),  or

96 - 16u = 48 + 8u,  or

48 = 24u.

Hence, u=2.

<U>Answer</U>.  the speed of the river is 2 km/h.
</pre>

For more similar solved problems of this type see the 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.


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>.