document.write( "Question 1176815: A motorboat travels 165 kilometers in 3 hours going upstream. It travels 207 kilometers going downstream in the same amount of time. 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 #853759 by n2(51) $\"\"$ $\"About$

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\n" ); document.write( "A motorboat travels 165 kilometers in 3 hours going upstream.
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\n" ); document.write( "What is the rate of the boat in still water and what is the rate of the current.
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document.write( "Let u be the rate of the boat in still water (in kilometers per hour), and \r\n" );
document.write( "let v be the rate of the current.\r\n" );
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document.write( "Then the effective rate of the boat downstream is (u+v) km/h,\r\n" );
document.write( "while its effective rate upstream is (u-v) km/h.\r\n" );
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document.write( "From the given data in the problem, we can calculate the effective rate downstream as\r\n" );
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document.write( "    u + v =  = 69 km/h\r\n" );
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document.write( "and the effective rate upstream as\r\n" );
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document.write( "    u - v =  = 55 km/h.\r\n" );
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document.write( "So, we have two equations\r\n" );
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document.write( "    u + v = 69,    (1)\r\n" );
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document.write( "    u - v = 55.    (2)\r\n" );
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document.write( "Find 'u' using the elimination method.  For it, add equations (1) and (2).\r\n" );
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document.write( "The terms 'v' and '-v' will cancel each other, and you will get\r\n" );
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document.write( "    2u = 69 + 55 = 124  --->  u = 124/2 = 62  km/h.\r\n" );
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document.write( "Now from equation (1) find\r\n" );
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document.write( "    v = 69 - 62 = 7 km/h.\r\n" );
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document.write( "At this point, the problem is solved completely.\r\n" );
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document.write( "ANSWER.  The rate of the boat in still water is 62 km/h,  and the rate of the current is 7 km/h.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full by a standard algebra way with complete explanations.\r
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