document.write( "Question 1050528: Flying with the wind, a plane flew 1200 mi in 5 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind \n" ); document.write( "

Algebra.Com's Answer #666099 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Flying with the wind, a plane flew 1200 mi in 5 h. Against the wind, the plane required 6 h to fly the same distance.
\n" ); document.write( "Find the rate of the plane in calm air and the rate of the wind
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document.write( "From the condition, you have these two equations\r\n" );
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document.write( " = u + v,   (1)   (flying with wind, the equation for the speed)\r\n" );
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document.write( " = u - v.   (2)   (flying against the wind)\r\n" );
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document.write( "Here u is the plane speed at no wind, v is the wind speed.\r\n" );
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document.write( "Simplify the system (1), (2):\r\n" );
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document.write( "u + v = 240,      (3)\r\n" );
document.write( "u - v = 200.      (4)\r\n" );
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document.write( "To solve it, add the equations (3) and (4). You will get\r\n" );
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document.write( "2u = 240 + 200  --->  2u = 440  --->  u =  = 220.\r\n" );
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document.write( "You just found the speed of the plane at no wind. It is 220 mph.\r\n" );
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document.write( "Now you can easily find v from (1): v = 240 - u = 240 - 220 - 20.\r\n" );
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document.write( "Thus the speed of the wind is 20 mph.\r\n" );
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document.write( "Answer.  Speed of the plane at no wind is 220 mph.  The speed of the wind is 20 mph.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For more similar problems and more details related to solutions see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems \r
\n" ); document.write( "\n" ); document.write( "    - More problems on upstream and downstream round trips \r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems solvable by quadratic equations \r
\n" ); document.write( "\n" ); document.write( "    - Selected problems from the archive on the boat floating Upstream and Downstream \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Travel and Distance problems\" of the section \"Word problems\".\r
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