document.write( "Question 437577: Flying against a headwind, a plane covers 900 miles in 2 hours. The return trip with a tailwind only takes an hour and a half. Find the speed of the wind, and the speed of the plane within the air mass. \n" ); document.write( "

Algebra.Com's Answer #853295 by ikleyn(53427) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Flying against a headwind, a plane covers 900 miles in 2 hours.
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\n" ); document.write( "Find the speed of the wind, and the speed of the plane within the air ma
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\n" ); document.write( "\n" ); document.write( "        The solution by @mananth has too much excessive calculations,\r
\n" ); document.write( "\n" ); document.write( "        which means that his computer code, which produces his text and calculations,\r
\n" ); document.write( "\n" ); document.write( "        is badly organized and creates anti-pedagigic narrative.\r
\n" ); document.write( "\n" ); document.write( "        As a result, the solution by @mananth scares readers and is a bad way to teach.\r
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\n" ); document.write( "\n" ); document.write( "        Below is my solution, which is a standard treatment of the problem without making unnecessary calculations.\r
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document.write( "Let u be the speed of the plane at no wind;\r\n" );
document.write( "    v be the speed of the wind.\r\n" );
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document.write( "The groundspeed flying against the wind is 900/2 = 450 mph.\r\n" );
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document.write( "The groundspeed flying with the wind is 900/1.5 = 600 mph.\r\n" );
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document.write( "The equations are\r\n" );
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document.write( "    u + v = 600    (1)   for flying with the wind\r\n" );
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document.write( "    u - v = 450    (2)   for flying against the wind\r\n" );
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document.write( "Adding equations (1) and (2), you get\r\n" );
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document.write( "    2u = 1050  --->  u = 1050/2 = 525 miles per hour.\r\n" );
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document.write( "Subtracting eq(2) from eq(1), you get\r\n" );
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document.write( "    2v = 150  --->  v = 150/2 = 75.\r\n" );
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document.write( "ANSWER.  The speed of the plane at no wind is 525 mph.  The rate of the wind is 75 mph.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved by the most straightforward way, without making unnecessary calculations.\r
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