document.write( "Question 1144659: A motorboat takes 5 hours to travel 150 km, going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #765823 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let  u  be the rate of the motorboat in still water (in kilometers per hour),\r\n" );
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document.write( "let  v  be the rate of the current.\r\n" );
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document.write( "Then the rate of the motorboat going downstream is  u+v  km/h,\r\n" );
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document.write( "while its rate going upstream is  u-v  km/h.\r\n" );
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document.write( "From the other side, the rate of the motorboat going downstream is   = 30 km/h.\r\n" );
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document.write( "Thus you have these two equations\r\n" );
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document.write( "    u + v = 50    (1)   (for the rate downstream),   and\r\n" );
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document.write( "    u - v = 30    (2)   (for the rate upstream).\r\n" );
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document.write( "To solve the system, add equations (1) and (2). You will get\r\n" );
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document.write( "    2u = 50 + 30 = 80;   hence,\r\n" );
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document.write( "     u           = 80/2 = 40 km/h.\r\n" );
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document.write( "Then from the equation (1),  v = 50 - u = 50 - 40 = 10 km/h.\r\n" );
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document.write( "ANSWER.  The the rate of the motorboat in still water is 40 km/h;  the rate of the current is  10 km/h.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a typical and standard Upstream and Downstream round trip word problem.\r
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\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, where you will find other similar solved problems with detailed explanations.\r
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\n" ); document.write( "\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
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\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
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\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
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\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
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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