Algebra.Com's Answer #847129 by ikleyn(52778)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 5 hours and 20 minutes,
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document.write( "but when there is a wind blowing from Penthaven to Jackson at 70 miles per hour, the trip takes 9 hours.
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document.write( "How many miles is the distance from Penthaven to Jackson?
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document.write( "Let \"d\" be the distance from Penthaven to Jackson, in miles.\r\n" );
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document.write( "Let \"u\" be the speed of the plane in still air (at no wind), in miles per hour.\r\n" );
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document.write( "Since the round trip is 5 hours and 20 minutes, we can write an equation\r\n" );
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document.write( "  = 5 hours,\r\n" );
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document.write( "or\r\n" );
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document.write( " 2d =  , d =  .\r\n" );
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document.write( "Next, the speed of the plane with the wind is u+70 mph and the travel time with the wind is \r\n" );
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document.write( "  =  =  .\r\n" );
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document.write( "Next, the speed of the plane against the wind is u-70 mph and the travel time against the wind is \r\n" );
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document.write( "  =  =  .\r\n" );
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document.write( "So, the time equation for the round trip with and against the wind is\r\n" );
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document.write( " + = 9.\r\n" );
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document.write( " +----------------------------------------------------------------------+\r\n" );
document.write( " | At this point, the setup is complete. Now our task is |\r\n" );
document.write( " | to solve this equation and to find the own speed \"u\" of the plane. |\r\n" );
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document.write( "For it, multiply both sides of this equation by 3*(u+70*(u-70). You will get\r\n" );
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document.write( " 8u(u+70) + 8u(u-70) = 9*3*(u+70)*(u-70),\r\n" );
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document.write( " 8u^2 + 560u + 8u^2 - 560u = 27*(u^2 - 4900),\r\n" );
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document.write( " 8u^2 + 8u^2 = 27u^2 - 27*4900,\r\n" );
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document.write( " 27*4900 = 27u^2 - 8u^2 - 8u^2\r\n" );
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document.write( " 27*4900 = 11u^2\r\n" );
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document.write( " u =  = 109.669 miles per hour.\r\n" );
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document.write( "Thus the own speed of the plane at no wind is 109.669 miles per hour.\r\n" );
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document.write( "Hence, the distance from Penthaven to Jackson is d = =  = 292.451 miles.\r\n" );
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document.write( "ANSWER. The distance from Penthaven to Jackson is about 292.5 miles.\r\n" );
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document.write( "Solved.\r
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document.write( "The method, which I showed in this post, is a normal, regular and standard method solving similar problems.\r
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document.write( "On the way, I fixed the error which tutor/professor Edwin made in his post.\r
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document.write( "I do not think that a/the school teacher would accept the solution presented by Edwin.\r
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