document.write( "Question 733604: a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow). what Will be the respective speed of the boat and the river (in km/hour)? \n" ); document.write( "

Algebra.Com's Answer #852780 by ikleyn(53427) $\"\"$ $\"About$

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\n" ); document.write( "a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow).
\n" ); document.write( "what will be the respective speed of the boat and the river (in km/hour)?
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document.write( "Let u be the speed of the boat at no current (in kilometers per hour),\r\n" );
document.write( "and let v be the rate of the current.\r\n" );
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document.write( "The speed of the boat with    the current is  96/8 = 12 km/h.\r\n" );
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document.write( "The speed of the boat against the current is  96/12 = 8 km/h.\r\n" );
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document.write( "The speed of the boat with    the current is  (u + v)  km/h.\r\n" );
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document.write( "The speed of the boat against the current is  (u - v)  km/h.\r\n" );
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document.write( "So, we have these equations\r\n" );
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document.write( "    u + v = 12,    (1)\r\n" );
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document.write( "    u - v =  8.    (2)\r\n" );
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document.write( "By adding equations (1) and (2),               we get  2u = 12 + 8 = 20;  hence,  u = 20/2 = 10 km/h.\r\n" );
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document.write( "By subtracting equation (2) from equation (1), we get  2v = 12 - 8 =  4;  hence,  v = 4/2 = 2 km/h.\r\n" );
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document.write( "ANSWER.  The speed of the boat at no current is 10km/h.\r\n" );
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document.write( "         The rate of the current is 2 km/h.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The answers in the post by @lynnlo are incorrect.\r
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