document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #686880 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A motor boat took 5 hours to travel 24km down the river to another town and to return. At another time the boat took
\n" ); document.write( "4 hours to travel 12km downstream and 24km upstream. Find the speed of the boat in still water and the speed of the river
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let \"u\" be the motorboat speed in still water, in mph, and\r\n" );
document.write( "Let \"v\" be the current rate.\r\n" );
document.write( "\r\n" );
document.write( "Then the motorboat effective speed downstream is (u+v) mph, while upstream (u-v) mph.\r\n" );
document.write( "\r\n" );
document.write( "The governing equations are\r\n" );
document.write( "\r\n" );
document.write( " = 5,    (1)\r\n" );
document.write( "\r\n" );
document.write( " = 4.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the system (1),(2), subtract (2) from (1). You will get\r\n" );
document.write( "\r\n" );
document.write( " = 1  ====>  u + v = 12.      (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Having this, from (1) you get\r\n" );
document.write( "\r\n" );
document.write( " =  = 5 - 2 = 3.  Hence,  u - v =  = 8.   (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Again,\r\n" );
document.write( "\r\n" );
document.write( "u + v = 12,    (3)\r\n" );
document.write( "u - v =  8.    (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add (3) and (4).  You will get \r\n" );
document.write( "\r\n" );
document.write( "2u = 12 + 8 = 20.   Hence,   u = 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from (3)  v = 12 - 10  = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The motorboat speed in still water is 10 mph.  The current speed is  2 mph.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For many similar problems see the lessons \r
\n" ); document.write( "\n" ); document.write( "- Wind and Current problems \r
\n" ); document.write( "\n" ); document.write( "- More problems on upstream and downstream round trips \r
\n" ); document.write( "\n" ); document.write( "- Wind and Current problems solvable by quadratic equations \r
\n" ); document.write( "\n" ); document.write( "- Unpowered raft floating downstream along a river\r
\n" ); document.write( "\n" ); document.write( "- Selected problems from the archive on the boat floating Upstream and Downstream \r
\n" ); document.write( "\n" ); document.write( "- Selected problems from the archive on a plane flying with and against the wind \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Travel and distance\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );