document.write( "Question 1064441: a motorboat can maintain a constant speed of 35 miles per hour relative to the water. the boat makes a trip upstream to a certain point in 30 minutes; the return trip takes 20 minutes. what is the soeed of the current? \n" ); document.write( "

Algebra.Com's Answer #679490 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "a motorboat can maintain a constant speed of 35 miles per hour relative to the water. the boat makes a trip upstream
\n" ); document.write( "to a certain point in 30 minutes; the return trip takes 20 minutes. what is the speed of the current?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let \"v\" be the speed of current, in miles per hour.\r\n" );
document.write( "\r\n" );
document.write( "Then the motorboat speed with    the current is 35+v miles per hour.  ( the speed relative to the bank of the river )\r\n" );
document.write( "     the motorboat speed against the current is 35-v miles per hour.  (-------------------- \" --------------------- )\r\n" );
document.write( "\r\n" );
document.write( "The distance for the trip downstream is the same as upstream:\r\n" );
document.write( "\r\n" );
document.write( " = .   (1)\r\n" );
document.write( "\r\n" );
document.write( " is  of an hour = 30 minutes,\r\n" );
document.write( "\r\n" );
document.write( " is  of an hour = 20 minutes.\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides of the eq.(1) by 6. You will get\r\n" );
document.write( "\r\n" );
document.write( "3*(35-v) = 2*(35+v),\r\n" );
document.write( "\r\n" );
document.write( "105 - 3v = 70 + 2v,\r\n" );
document.write( "\r\n" );
document.write( "105 - 70 = 2v + 3v,\r\n" );
document.write( "\r\n" );
document.write( "35 = 5v  ---->  v =  = 7 mph.\r\n" );
document.write( "\r\n" );
document.write( "Answer. The current speed is 7 mph. The distance is  = 14 miles.\r\n" );
document.write( "\r\n" );
document.write( "Check.  Time upstream  =  =  of an hour.\r\n" );
document.write( "\r\n" );
document.write( "        Time downstream  =  =  of an hour.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you send me your comments/questions, please include the ID number of this problem (# 1064441) in order I could identify it.\r
\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( "    - 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( " \n" ); document.write( "

\n" );