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 #853769 by ikleyn(53619) $\"\"$ $\"About$

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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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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "This solution produces the same answer as in the post by @mananth, but has an advantage
\n" ); document.write( "that it does not contain excessive calculations that the solution by @mananth has.\r
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\n" ); document.write( "\n" ); document.write( "We, the tutors, write here our solutions not only to get certain numerical answer.
\n" ); document.write( "We write to teach - and, in particular, to teach solving in a right style.\r
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\n" ); document.write( "\n" ); document.write( "This style solving presented in my post, is straightforward with no logical loops.
\n" ); document.write( "The solution presented in the post by @mananth has two logical loops.\r
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document.write( "    One loop in the @mananth post is writing\r\n" );
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document.write( "        42/(x+y) = 3.5   --->   divide by 3.5  12/(x+y) = 1  --->   x+y = 12,\r\n" );
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document.write( "    while in my solution I simply write for the effective rate \r\n" );
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document.write( "        x + y = 42/3.5 = 12.\r\n" );
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document.write( "    Second loop in the @mananth post is writing\r\n" );
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document.write( "                       18/(x-y) = 3   --->   divide by 3  6/(x-y) = 1  --->   x-y = 6,\r\n" );
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document.write( "    while in my solution I simply write for the effective rate upstream\r\n" );
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document.write( "        x - y = 18/3 = 6.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is why I present my solution here and why I think it is better than the solution by @mananth:
\n" ); document.write( "- because it teaches students to present their arguments in a straightforward way, without logical zigzags.\r
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\n" ); document.write( "\n" ); document.write( "@mananth repeats his construction of solution with no change for all similar problems on floating
\n" ); document.write( "with and against the current simply because his COMPUTER CODE is written this way.
\n" ); document.write( "But this way is not pedagogically optimal - in opposite, it is pedagogically imperfect.\r
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