document.write( "Question 1189181: Two kayakers paddle 18 km downstream with the current in the same time it takes them to go 8 km upstream against the current. The rate of the current is 3 km/hr. What is the rate of the kayakers in still water?\r
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Algebra.Com's Answer #820448 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Two kayakers paddle 18 km downstream with the current in the same time it takes them to go 8 km upstream against the current.
\n" ); document.write( "The rate of the current is 3 km/hr. What is the rate of the kayakers in still water?
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\n" ); document.write( "Downstream: Distance (km)? Rate (km/hr)? Time (hr)
\n" ); document.write( "Upstream: Distance (km)? Rate (km/hr)? Time (hr)
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document.write( "Let x be the rate of the kayakers in still water.\r\n" );
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document.write( "Then the rate paddling downstream is (x+3) km/h; time paddling downstream is   hours.\r\n" );
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document.write( "     the rate paddling   upstream is (x-3) km/h; time paddling   upstream is   hours.\r\n" );
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document.write( "The times are the same, giving this time equation\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Solve by cross-multiplying\r\n" );
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document.write( "    18*(x-3) = 8*(x+3)\r\n" );
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document.write( "    18x - 54 = 8x + 24\r\n" );
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document.write( "    18x - 8x = 24 + 54\r\n" );
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document.write( "       10x   =   78\r\n" );
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document.write( "         x   =  78/10 = 7.8 km/h\r\n" );
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document.write( "ANSWER.  The rate of kayakers in still water is  7.8 km/h.\r\n" );
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document.write( "CHECK.  The time paddling downstream is   =  hours =  =  hours = 100 minutes.\r\n" );
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document.write( "        The time paddling   upstream is   =  =  hours =   hours = 100 minutes.   ! Correct ! \r\n" );
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