document.write( "Question 1177332: A kayak can travel 24 miles downstream in 2 hours, while it would take 12 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water, and let c represent the speed of the current. \n" ); document.write( "

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\n" ); document.write( "A kayak can travel 24 miles downstream in 2 hours, while it would take 12 hours to make the same trip upstream.
\n" ); document.write( "Find the speed of the kayak in still water, as well as the speed of the current.
\n" ); document.write( "Let k represent the speed of the kayak in still water, and let c represent the speed of the current.
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document.write( "Let k be the rate of the kayak in still water (in miles per hour)\r\n" );
document.write( "and c be the rate of the current (in the same units).\r\n" );
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document.write( "Then the effective rate of the kayak downstream is k + c\r\n" );
document.write( "and  the effective rate of the kayak   upstream is k - c.\r\n" );
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document.write( "From the problem, the effective rate of the kayak downstream is the distance of 24 miles \r\n" );
document.write( "divided by the time of 2 hours   = 12 mph.\r\n" );
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document.write( "                  The effective rate of the kayak upstream is the distance of 24 miles \r\n" );
document.write( "divided by the time of 12 hours   = 2 mph.\r\n" );
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document.write( "So, we have two equations to find 'k' and 'c'\r\n" );
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document.write( "    k + c = 12,    (1)\r\n" );
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document.write( "    k - c =  2.    (2)\r\n" );
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document.write( "To solve, add equations (1) and (2).  The terms 'c' and '-c' will cancel each other, and you will get\r\n" );
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document.write( "    2k = 12 + 2 = 14  --->   k = 14/2 = 7.\r\n" );
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document.write( "Now from equation (1)\r\n" );
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document.write( "     v = 12 - u = 12 - 7 = 5.\r\n" );
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document.write( "ANSWER.  The rate of the kayak in still water is 7 mph.  The rate of the current is 5 mph km/h.\r\n" );
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