document.write( "Question 980198: A can clean a room in 5 hours. After A worked alone for 2 hours, B joined him. Together they finished cleaned the room in an hour. How long would it take B to clean the room? \n" ); document.write( "
Algebra.Com's Answer #601404 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Oh darn it! She's already done it for you before I could post this!
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document.write( "To prevent students from merely turning in my answers to multiple choice\r\n" );
document.write( "homework problems, instead of doing the exact same problems, I do a\r\n" );
document.write( "problem EXACTLY similar to it, but changing the numbers.  So the problem\r\n" );
document.write( "I will solve is this one. You can use it as an exact model for your problem.\r\n" );
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\n" ); document.write( "A can do a job in 10 hours. After A worked alone for 2 hours, B joined him.
\n" ); document.write( "Together they finished the job in 3 hours. How long would it take B to do
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document.write( "Begin with this statement:\r\n" );
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\n" ); document.write( "A can do a job in 10 hours.
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document.write( "Therefore A's work rate is 1 job per 10 hours or 1/10 job per hour. \r\n" );
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\n" ); document.write( "How long would it take B to do the job alone?
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document.write( "Suppose it would take B x hours to do the job alone.\r\n" );
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document.write( "Then B's work rate is 1 job per x hours or 1/x job per hour\r\n" );
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\n" ); document.write( "After A worked alone for 2 hours,
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document.write( "The part of the job that A did in those 2 hours is found by RATExTIME\r\n" );
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document.write( "So in those 2 hours A did (1/10)(2) = 2/10 = 1/5 of the job.\r\n" );
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document.write( "That left 1-2/5 = 5/5-1/5 = 4/5ths of the job still to be done.\r\n" );
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\n" ); document.write( "B joined him.
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document.write( "So then their combined rate was the sum of their rates (1/10 + 1/x).\r\n" );
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\n" ); document.write( "Together they finished the job in 3 hours.
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document.write( "The part of the job that they did in those 3 hours is also found by\r\n" );
document.write( "RATExTIME, and the part they did together must equal to the remaining \r\n" );
document.write( "4/5 of the job.  So the equation is \r\n" );
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document.write( "             (1/10 + 1/x)(3) = 4/5\r\n" );
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document.write( "               3(1/10 + 1/x) = 4/5\r\n" );
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document.write( "                  3/10 + 3/x = 4/5\r\n" );
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document.write( "Multiply through by LCD of 10x\r\n" );
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document.write( "                     3x + 30 = 8x\r\n" );
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document.write( "                          30 = 5x\r\n" );
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document.write( "                           6 = x\r\n" );
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document.write( "So it would take B 6 hours to do the job alone\r\n" );
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document.write( "Now use this as an exact model to solve your problem.                                \r\n" );
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document.write( "Edwin
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