document.write( "Question 299199: An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed? \n" ); document.write( "

Algebra.Com's Answer #854277 by ikleyn(53828) $\"\"$ $\"About$

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\n" ); document.write( "An airplane took 4 hours to fly 1200 miles agianst a headwind. The return trip with the wind took 3 hours.
\n" ); document.write( "Find the speed of the plane in still air and the speed of the wind.
\n" ); document.write( "What is the speed of the $\"highlight%28cross%28wind%29%29\"$ plane in still air? What is the wind speed?
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\n" ); document.write( "\n" ); document.write( "        To the visitor: \r
\n" ); document.write( "\n" ); document.write( "                \"against a headwind\" is not a good term. Say simply \"against the wind\".\r
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\n" ); document.write( "\n" ); document.write( "        Notice that I edited your post to make sense from nonsense.\r
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\n" ); document.write( "\n" ); document.write( "        The solution by @mananth uses the \"zigzag\" logic, which is not recommended.\r
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\n" ); document.write( "\n" ); document.write( "        To teach in a right way, I use a straightforward logic without zigzags. It is the style, which is recommended.\r
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document.write( "Let the rate of the plane in still air be x miles per hour.\r\n" );
document.write( "Let the rate of the wind be y miles per hour.\r\n" );
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document.write( "The effective rate of the plane against the wind is  (x-y).\r\n" );
document.write( "According to the problem, it is \r\n" );
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document.write( "    x - y =  = 300 mph.      (the distance divided by the time)\r\n" );
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document.write( "The effective rate of the plane with the wind is  (x+y).\r\n" );
document.write( "According to the problem, it is \r\n" );
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document.write( "    x + y =  = 400 mph.      (the distance divided by the time)\r\n" );
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document.write( "Thus you have these two equations to find x and y\r\n" );
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document.write( "    x + y = 400,    (1)\r\n" );
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document.write( "    x - y = 300.    (2)\r\n" );
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document.write( "To find x, add equations (1) and (2).  You will get\r\n" );
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document.write( "    2x = 400 + 300 = 700,  x = 700/2 = 350.\r\n" );
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document.write( "To find y, subtract equation (2) from equation (1).  You will get\r\n" );
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document.write( "    2y = 400 - 300 = 100,  y = 100/2 = 50.\r\n" );
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document.write( "ANSWER.  The rate of the plane in still air is 350 mph.\r\n" );
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document.write( "         The rate of the wind is 50 mph.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved by a standard way using a straightforward logic.\r
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