document.write( "Question 1095637: A motorboat takes 3 hours to travel 108km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #710129 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Let u be the motorboat speed in still water and v be the current rate.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The effective speed going upstream is \r\n" );
document.write( "\r\n" );
document.write( " =  = 36 km/h.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the DIFFERENCE of the motorboat speed in still water and the rate of the current. It gives you your first equation\r\n" );
document.write( "\r\n" );
document.write( "u - v = 36.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The effective speed going downstream is \r\n" );
document.write( "\r\n" );
document.write( " =  = 54 km/h.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the SUM of the motorboat speed in still water and the rate of the current. It gives you your second equation\r\n" );
document.write( "\r\n" );
document.write( "u + v = 54.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you have this system of two equations in 2 unknowns\r\n" );
document.write( "\r\n" );
document.write( "u - v = 36,    (1)   and\r\n" );
document.write( "u + v = 54.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add the two equations. You will get\r\n" );
document.write( "\r\n" );
document.write( "2u = 36 + 54 = 90  ====>  u =  = 45 km/h.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, you just found the speed of the motorboat in still water.  It is  45 km/h.\r\n" );
document.write( "\r\n" );
document.write( "Then from the equation (2) you get  v = 54 = 45 = 9 km/h is the current rate.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The speed of the motorboat in still water is  45 km/h.\r\n" );
document.write( "\r\n" );
document.write( "         The current rate is 9 km/h.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------
\n" ); document.write( "It is a typical and standard Upstream and Downstream round trip word problem.\r
\n" ); document.write( "\n" ); document.write( "You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in 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( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
\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 textbook under the section \"Word problems\", the topic \"Travel and Distance problems\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );