document.write( "Question 288541: A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 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 #854236 by n2(88) $\"\"$ $\"About$

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\n" ); document.write( "A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream.
\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 motorboat in still water (in miles per hour)\r\n" );
document.write( "and v be the rate of the current (in the same units).\r\n" );
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document.write( "Then the effective rate of the motorboat downstream is  u + v  miles per hour,\r\n" );
document.write( "and  the effective rate of the motorboat   upstream is  u - v  miles per hour.\r\n" );
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document.write( "From the problem, the effective rate of the motorboat downstream is the distance of 256 miles \r\n" );
document.write( "divided by the time of 2 hours   = 128 mph.\r\n" );
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document.write( "                  The effective rate of the motorboat upstream is the distance of 256 miles \r\n" );
document.write( "divided by the time of 4 hours   = 64 mph.\r\n" );
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document.write( "So, we have two equations to find 'u' and 'v'\r\n" );
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document.write( "    u + v = 128,    (1)\r\n" );
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document.write( "    u - v =  64.    (2)\r\n" );
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document.write( "To solve, add equations (1) and (2).  The terms 'v' and '-v' will cancel each other, and you will get\r\n" );
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document.write( "    2u = 128 + 64 = 192  --->   u = 192/2 = 96.\r\n" );
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document.write( "Now from equation (1)\r\n" );
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document.write( "     v = 128 - u = 128 - 96 = 32.\r\n" );
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document.write( "ANSWER.  Under given conditions, the rate of the motorboat in still water is 96 mph.  \r\n" );
document.write( "         The rate of the current is 32 mph km/h.\r\n" );
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