document.write( "Question 288541: A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #854235 by ikleyn(53875) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream.
\n" ); document.write( "What is the rate of the boat in still water and what is the rate of the current?
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\n" ); document.write( "\n" ); document.write( "        The solution by @mananth in his post has arithmetic errors that lead to wrong answer.\r
\n" ); document.write( "\n" ); document.write( "        In addition, the form of his presentation is MONSTROUS, which can not serve as a tool\r
\n" ); document.write( "\n" ); document.write( "        for teaching or learning.\r
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\n" ); document.write( "\n" ); document.write( "        Therefore, I came with my alternative solution to replace the post by @mananth.\r
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document.write( "Let u be the rate of the motorboat in still water (in miles per hour)\r\n" );
document.write( "and v 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  u + v  miles per hour,\r\n" );
document.write( "and  the effective rate of the motorboat   upstream is  u - v  miles per hour.\r\n" );
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document.write( "From the problem, the effective rate of the motorboat downstream is the distance of 256 miles \r\n" );
document.write( "divided by the time of 2 hours   = 128 mph.\r\n" );
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document.write( "                  The effective rate of the motorboat upstream is the distance of 256 miles \r\n" );
document.write( "divided by the time of 4 hours   = 64 mph.\r\n" );
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document.write( "So, we have two equations to find 'u' and 'v'\r\n" );
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document.write( "    u + v = 128,    (1)\r\n" );
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document.write( "    u - v =  64.    (2)\r\n" );
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document.write( "To solve, add equations (1) and (2).  The terms 'v' and '-v' will cancel each other, and you will get\r\n" );
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document.write( "    2u = 128 + 64 = 192  --->   u = 192/2 = 96.\r\n" );
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document.write( "Now from equation (1)\r\n" );
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document.write( "     v = 128 - u = 128 - 96 = 32.\r\n" );
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document.write( "ANSWER.  Under given conditions, the rate of the motorboat in still water is 96 mph.  \r\n" );
document.write( "         The rate of the current is 32 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( "The reader should know that this problem and this type of problems @mananth \"solves\" using his computer code.\r
\n" ); document.write( "\n" ); document.write( "So, his posts are not a production of a human - they are production of a computer code,\r
\n" ); document.write( "\n" ); document.write( "and @mananth himself does not check his production (and even does not read it).\r
\n" ); document.write( "\n" ); document.write( "His computer code for this type of problem is written by an incorrect way, so every time \r
\n" ); document.write( "\n" ); document.write( "it produces the same type malformed version.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, at every appearance, I come and fix/repair his presentation to make sense from badly presented solution
\n" ); document.write( "and to keep this forum relatively clean from garbage.\r
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\n" ); document.write( "\n" ); document.write( "@ikleyn\r
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POST-SOLUTION note:

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\n" ); document.write( "\n" ); document.write( "The given data in the problem are not realistic, and lead to unrealistic final answer.\r
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\n" ); document.write( "\n" ); document.write( "Indeed, without explanations, it is obvious that the rate of the current of 32 miles per hour is too much
\n" ); document.write( "in order for some real motorboat would be able to move against the current, if it is not a fantastic story.\r
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\n" ); document.write( "\n" ); document.write( "A normal and regular speed of the current in such problem is, usually, not more that 4 miles per hour.
\n" ); document.write( "This is a typical current speed for lowland rivers.\r
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\n" ); document.write( "\n" ); document.write( "But this defect is not a defect of the solution - it is a product of the defective
\n" ); document.write( "and unsatisfactory job of the Math composer, i.e. the person, who created this Math problem.\r
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