document.write( "Question 1179660: A motorboat traveling with the current went 42 mi in 3.5 h. Traveling against the current, the boat went 18 mi in 3 h. Find the rate of the boat in calm water and the rate of the current. \n" ); document.write( "

Algebra.Com's Answer #853770 by n2(54) $\"\"$ $\"About$

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\n" ); document.write( "A motorboat traveling with the current went 42 mi in 3.5 h. Traveling against the current, the boat went 18 mi in 3 h.
\n" ); document.write( "Find the rate of the boat in calm water and the rate of the current.
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document.write( "Let x be the rate of the motorboat 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 motorboat downstream is x + y\r\n" );
document.write( "and  the effective rate of the motorboat   upstream is x - y.\r\n" );
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document.write( "From the problem, the effective rate of the motorboat downstream is the distance of 42 miles \r\n" );
document.write( "divided by the time of 3.5 hours   = 12 mph.\r\n" );
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document.write( "                  The effective rate of the motorboat upstream is the distance of 18 miles \r\n" );
document.write( "divided by the time of 3 hours   = 6 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( "    x + y = 12,    (1)\r\n" );
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document.write( "    x - y =  6.    (2)\r\n" );
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document.write( "To solve, add equations (1) and (2).  The terms 'y' and '-y' will cancel each other, and you will get\r\n" );
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document.write( "    2x = 12 + 6 = 18  --->   x = 18/2 = 9.\r\n" );
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document.write( "Now from equation (1)\r\n" );
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document.write( "     v = 12 - u = 12 - 9 = 3.\r\n" );
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document.write( "ANSWER.  The rate of the motorboat in still water is 9 mph.  The rate of the current is 3 mph km/h.\r\n" );
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