document.write( "Question 1048168: If a plane can travel 500 miles per hour with the wind and 400 miles per hour against the wind, find the speed of the plan without a wind and speed with the wind.
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Algebra.Com's Answer #663739 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "If a plane can travel 500 miles per hour with the wind and 400 miles per hour against the wind,
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document.write( "If \"u\" is the plane speed without a wind and \"v\" is the speed of the wind, then\r\n" );
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document.write( "1.  The speed of a plane relative to the Earth (relative to the ground) is \r\n" );
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document.write( "    u + v when it flying with the wind,  and\r\n" );
document.write( "    u - v when it flying against the wind.\r\n" );
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document.write( "2. So, you are given \r\n" );
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document.write( "   u + v = 500,   (1)\r\n" );
document.write( "   u - v = 400.   (2)\r\n" );
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document.write( "3.  Add these two equations. You will get\r\n" );
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document.write( "    2u = 500 + 400  --->  2u = 900  --->  u =  = 450\r\n" );
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document.write( "         Thus you just found the speed of the airplane at no wind. It is 450 miles per hour.\r\n" );
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document.write( "    Now you will easily find from (1) v = 500 - 450 = 50.\r\n" );
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document.write( "        So, the speed of wind is 50 mph.\r\n" );
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document.write( "Answer.  The speed of the airplane at no wind is 450 miles per hour.\r\n" );
document.write( "         The speed of wind is 50 mph.\r\n" );
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