document.write( "Question 1007654: A person rowed their boat downstream for 100 miles and they took 2 hours. Returning upstream, the trip took 2 hours and 40 minutes.\r
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Algebra.Com's Answer #853922 by n2(78) $\"\"$ $\"About$

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\n" ); document.write( "A person rowed their boat downstream for 100 miles and they took 2 hours.
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document.write( "Let x be the rate of the boat in still water (in miles per hour)\r\n" );
document.write( "and y be the rate of the current (in the same units).\r\n" );
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document.write( "Then the effective rate of the boat downstream is x + y\r\n" );
document.write( "and  the effective rate of the boat   upstream is x - y.\r\n" );
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document.write( "From the problem, the effective rate of the boat downstream is the distance of 100 miles \r\n" );
document.write( "divided by the time of 2 hours   = 50 mph.\r\n" );
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document.write( "                  The effective rate of the boat upstream is the distance of 100 miles \r\n" );
document.write( "divided by the time of 2 hours and 40 minute, or  2 hours, or   hours\r\n" );
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document.write( "     =  = 37.5 mph\r\n" );
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document.write( "So, we have two equations for  'x'  and  'y'\r\n" );
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document.write( "    x + y = 50,      (1)\r\n" );
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document.write( "    x - y = 37.5.    (2)\r\n" );
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document.write( "To find 'y', subtract equations (2) from equation (1).  The terms 'x' and 'x' will cancel each other, and you will get\r\n" );
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document.write( "    2y = 50 - 37.5 = 12.5  --->   y = 12.5/2 = 6.25.\r\n" );
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document.write( "At this point, the solution is complete.\r\n" );
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document.write( "ANSWER.  The rate of the current is 6.25 miles per hour.\r\n" );
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