Question 1111883
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<pre>
Let L be the distance between the cities (in some units, miles or kilometers - IT DOES NOT MATTER, as you will see further).

Let u be the speed of the boat in still water (in the CORRESPONDING units), and

let v be the rate of the current (in the same units).


You are given

{{{L/(u+v)}}} = 3  hours    (1)   (rowing downstream)

{{{L/(u+v)}}} = 4  hours    (2)   (rowing   upstream)


From these equations

3*(u+v) = L                 (1')
4*(u-v) = L                 (2')


or, equivalently


3u + 3v = L                 {1'')
4u - 4v = L                 (2'')


What I need is to find the ratio  {{{L/v}}}.  It is EXACTLY the time a piece of driftwood to float downstream from Bowraville to Macksville,
which is under the question.


For it, I am going to eliminate the variable "u" from the equations (1'') and (2'') and to express "v" via L (or, conversely, express L via "v").


So I multiply eq(1'') by 4 (both sides) and multiply eq(2'') by 3 (both sides). I will get

12u - 12v = 3L     (3)
12u + 12v = 4L     (4)


Now subtract eq(3) from eq(4). You will get

24v = L,   which implies  {{{L/v}}} = 24.


It gives the <U>ANSWER</U>:  it will take 24 hours for a piece of driftwood to float downstream from Bowraville to Macksville

(since this piece moves with the rate of the current).
</pre>

Solved.


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It is a &nbsp;CLASSIC &nbsp;"downstream-upstream" &nbsp;problem.


See the lesson

&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>

in this site.


You can find many other 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.
The relevant lesson is marked (*) in this list.


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.