document.write( "Question 850681: A machine P can print one math book in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one math book) be finished ? \n" ); document.write( "

Algebra.Com's Answer #854122 by MathTherapy(10803) $\"\"$ $\"About$

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document.write( "A machine P can print one math book in 8 hours, machine Q can print the same number of \r\n" );
document.write( "books (this author believes this should be PAGES) in 10 hours while machine R can print them in\r\n" );
document.write( "12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the\r\n" );
document.write( "remaining two machines complete work. Approximately at what time will the work (to print one\r\n" );
document.write( "math book) be finished ?\r\n" );
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document.write( "The other person's answer, \"approximately\" 12:03 PM....\", is WRONG!!\r\n" );
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document.write( "Machine P does the job (prints book) in 8 hrs, or does  of entire job in 1 hr\r\n" );
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document.write( "Machines P and Q do the job (print book) in 10 and 12 hrs, respectively\r\n" );
document.write( "Then each does  and  of entire job in 1 hr, respectively\r\n" );
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document.write( "In 2 hours, the 3 machines complete  =  =  =  = \r\n" );
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document.write( "Let the time it takes Q and R to complete the job, be T\r\n" );
document.write( "Then working together, Q and R completes  of the job\r\n" );
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document.write( "We then get the following COMPLETE-JOB equation: T1(rates) + T2(rates) = 1 (entire job), OR\r\n" );
document.write( "                                        Fraction completed + Remaining Fraction = 1 (entire job). This produces: \r\n" );
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document.write( "                                                          37 + 6T + 5T = 60 ---- Multiplying by LCD, 60\r\n" );
document.write( "                                                              37 + 11T = 60\r\n" );
document.write( "                                                                   11T = 60 - 37\r\n" );
document.write( "                                                                   11T = 23\r\n" );
document.write( "Time it takes Q and R to complete the job, after P, Q, and R worked together for 2 hrs, or \r\n" );
document.write( "or 2 hrs, 5.5 minutes, approximately.\r\n" );
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document.write( "Finally, 2 hrs, 5.5 minutes after 11:00 a.m. takes us to 1:05.5, or approximately 1:06 p.m.\r\n" );
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document.write( "ANECDOTE\r\n" );
document.write( "As seen above, the other person's approximated 1-hr claim is INVALID. The 3 machines completed  of job in 2\r\n" );
document.write( "hours, which leaves  of the job, incomplete. Does it make sense that 3 machines take 2 hours to complete ,\r\n" );
document.write( "or >  of the job, but 2 of the 3 machines take just 1 hour to complete the remaining  (approximation),\r\n" );
document.write( "especially when the FASTEST of the 3, P, is no longer working?

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