document.write( "Question 1158748: A kayak can travel 18 miles downstream in 3 hours, while it would take 9 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( "

Algebra.Com's Answer #781736 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "    18/3 = 6 = k + c   (1)    (the effective speed downstream)\r\n" );
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document.write( "    18/9 = 2 = k - c   (2)    (the effective speed upstream)\r\n" );
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document.write( "Again, you have these two equations\r\n" );
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document.write( "    k + c = 6          (1)\r\n" );
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document.write( "    k - c = 2          (2)\r\n" );
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document.write( "Add these two equations. You will get\r\n" );
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document.write( "    2k    = 6 + 2 = 8;  hence  k = 8/2 = 4  is the speed of the kayak in still water.\r\n" );
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document.write( "Next, substitute  k= 4 into equation (1).  You will get\r\n" );
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document.write( "    4 + c = 6,  which  implies  c = 6-4 = 2.\r\n" );
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document.write( "ANSWER.  The kayak speed in still water is 4 miles per hour.\r\n" );
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document.write( "         The speed of the current is  2 miles per hour.\r\n" );
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