document.write( "Question 1147577: A river boat takes 4 hours when going with the current from point A to point B (along a straight river), while its engine is using maximum power (the boat is at full speed). It takes 8 hours for the boat to go back against the current from point B to point A at full speed. How long will it take for the same boat to go back with the current from point A to point B with its engine off? \n" ); document.write( "

Algebra.Com's Answer #768944 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let \"d\" be the distance between the points A and B along the river.\r\n" );
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document.write( "Let \"u\" be the motorboat speed in still water and let \"v\" be the speed of the current.\r\n" );
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document.write( "Then the effective speed of the motorboat with the current (downstream) is \r\n" );
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document.write( "    u + v =      (1)\r\n" );
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document.write( "while the effective speed against the current (upstream) is \r\n" );
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document.write( "    u - v = .    (2)\r\n" );
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document.write( "Subtract equation (2) from equation (1).  You will get\r\n" );
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document.write( "       2v =  =  -  = .\r\n" );
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document.write( "Hence,  v = .\r\n" );
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document.write( "Thus the current speed is    units of length per hour.\r\n" );
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document.write( "Now notice, that the motorboat with the engine turned off travels along the river with the effective speed, \r\n" );
document.write( "EQUAL to the speed of the current.\r\n" );
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document.write( "It means that the motorboat with the engine turned off will cover the distance \"d\" from A to B in\r\n" );
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document.write( "     = 16 hours.\r\n" );
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document.write( "It is the ANSWER  to the problem's question:  16 hours.\r\n" );
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\n" ); document.write( "\n" ); document.write( ".........................\r
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\n" ); document.write( "\n" ); document.write( "In order for you better understand the power and beauty of this solution, notice the following:\r
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document.write( "    1)  the solution and the answer DO NOT DEPEND on units of length (!).\r\n" );
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document.write( "    2)  the solution and the answer are valid for any value of \"d\", the distance between the points (!) \r\n" );
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document.write( "    3)  The idea of the solution is simple: first find the speed of the current in terms of \"d\";\r\n" );
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document.write( "        then take into account that the speed of the motorboat with the engine turned off is precisely equal\r\n" );
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document.write( "        to the speed of the current.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is typical problem for the school Math circle level.\r
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\n" ); document.write( "\n" ); document.write( "In this site, there is a block of lessons on Travel and Distance for upstream and downstream round trips\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
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\n" ); document.write( "\n" ); document.write( "Of these lessons, the lesson marked (*) is exactly and precisely about THIS problem.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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\n" ); document.write( "\n" ); document.write( "Come again to this forum soon to learn something new (!)\r
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