Question 1071978
.
A motor boat took 5 hours to travel 24km down the river to another town and to return. At another time the boat took 
4 hours to travel 12km downstream and 24km upstream. Find the speed of the boat in still water and the speed of the river
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<pre>
Let "u" be the motorboat speed in still water, in mph, and
Let "v" be the current rate.

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

The governing equations are

{{{24/(u+v) + 24/(u-v)}}} = 5,    (1)

{{{12/(u+v) + 24/(u-v)}}} = 4.    (2)


To solve the system (1),(2), subtract (2) from (1). You will get

{{{12/(u+v)}}} = 1  ====>  u + v = 12.      (3)


Having this, from (1) you get

{{{24/(u-v)}}} = {{{5 - 24/(u+v)}}} = 5 - 2 = 3.  Hence,  u - v = {{{24/3}}} = 8.   (4)


Again,

u + v = 12,    (3)
u - v =  8.    (4)


Add (3) and (4).  You will get 

2u = 12 + 8 = 20.   Hence,   u = 10.


Then from (3)  v = 12 - 10  = 2.


<U>Answer</U>.  The motorboat speed in still water is 10 mph.  The current speed is  2 mph.
</pre>

Solved.


For many similar problems see the lessons 

- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

- <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> 

- <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> 

- <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>

- <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> 

- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-plane-flying-with-and-against-the-wind.lesson>Selected problems from the archive on a plane flying with and against the wind</A> 

in this site.



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 online textbook under the topic "<U>Travel and distance</U>".