document.write( "Question 264864: an airplane travels 900 miles from houston to miami in 6 hors against the wind.on its return trip, with the wind, it takes only 5 hours. find the rate of the airplane with no wind. find the rate of the wind \n" ); document.write( "

Algebra.Com's Answer #854033 by ikleyn(53750) $\"\"$ $\"About$

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\n" ); document.write( "an airplane travels 900 miles from Houston to Miami in 6 hors against the wind.
\n" ); document.write( "on its return trip, with the wind, it takes only 5 hours.
\n" ); document.write( "find the rate of the airplane with no wind. find the rate of the wind
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @mananth is correct: it leads to correct answer.\r
\n" ); document.write( "\n" ); document.write( "        But the @Mananth' solution is badly organized.\r
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\n" ); document.write( "\n" ); document.write( "        One of the goals of such problems is to teach students to present their solution in perfect \r
\n" ); document.write( "\n" ); document.write( "        form with straightforward logic.\r
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\n" ); document.write( "\n" ); document.write( "        Therefore I place my solution here.\r
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document.write( "Let the ground speed be x\r\n" );
document.write( "And the wind   speed be y\r\n" );
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document.write( "AGAINST WIND\r\n" );
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document.write( "Distance = 900 miles.\r\n" );
document.write( "Rate = Distance/time\r\n" );
document.write( "x-y = 900/6 = 150 miles per hour.\r\n" );
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document.write( "WITH WIND\r\n" );
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document.write( "Distance = 900 miles.\r\n" );
document.write( "Rate = Distance/time\r\n" );
document.write( "x + y = 900/5 = 180  miles per hour.\r\n" );
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document.write( "Thus we have a system of two equations for unknowns x and y\r\n" );
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document.write( "    x - y = 150    (1)\r\n" );
document.write( "    x + y = 180    (2)\r\n" );
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document.write( "To find 'x', add the equations.  You will get\r\n" );
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document.write( "    2x = 150 + 180 = 330  --->  x = 330/2 = 165.\r\n" );
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document.write( "To find 'y', substitute x = 165 in equation (2)\r\n" );
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document.write( "    165 + y = 180  --->  y = 180 - 165 = 15.\r\n" );
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document.write( "ANSWER.  The rate of the plane with no wind is 165 miles per hour.\r\n" );
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document.write( "         The rate of the wind is 15 miles per hour.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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