document.write( "Question 813821: A,B, and C could finish a job alone in 5 hours. The three started together at 8AM but B rested at 9AM and resumed working at 9:30 AM. At what time they will finish the work? \n" ); document.write( "
Algebra.Com's Answer #490080 by Edwin McCravy(20066)\"\" \"About 
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A,B, and C could finish a job alone in 5 hours. The three started together at 8AM but B rested at 9AM and resumed working at 9:30 AM. At what time they will finish the work?
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document.write( "The other tutor with his equation\r\n" );
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document.write( "t/5 + (t-.5)/5 + t/5 = 1\r\n" );
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document.write( "is wrong, first because the first term \r\n" );
document.write( "should be 1/5, not t/5, because from 8 till 9 \r\n" );
document.write( "is 1 hour, not t hours.  His second term is \r\n" );
document.write( "wrong because B was not working during that \r\n" );
document.write( "half hour from 9 till 9:30, so he couldn't use \r\n" );
document.write( "1/5.  The last term is wrong because it is not \r\n" );
document.write( "known that they worked as long after 9:30 as \r\n" );
document.write( "they worked before 9. \r\n" );
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document.write( "It is not known how long it would takes B working\r\n" );
document.write( "alone to do the job.  This is another variable.  \r\n" );
document.write( "If B takes x hours to do the job, then he does \r\n" );
document.write( "1/xths of the joh in one hour.  So if B had been \r\n" );
document.write( "working that half hour instead of resting, they \r\n" );
document.write( "would have completed (1/2)(1/5) or 1/(10)ths of \r\n" );
document.write( "the job during that half hour.  However, since B \r\n" );
document.write( "didn't work during that half hour we must subtract \r\n" );
document.write( "the portion of the job he would have done, which \r\n" );
document.write( "is (1/2)(1/x) = 1/(2x) so from 9:00 to 9:30 A and C\r\n" );
document.write( "only did [1/10 - 1/(2x)] = (2x-10)/(2x) = 2(x-5)/(2x) \r\n" );
document.write( "= (x-5)/x of the job.\r\n" );
document.write( "was done.\r\n" );
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document.write( "Now we don't know how long it will take after 9:30\r\n" );
document.write( "to finish the job, for that depends on how fast B\r\n" );
document.write( "works.   So we have to use another unknown\r\n" );
document.write( "for that, y hours.  Let y = the time after 9:30 that \r\n" );
document.write( "it takes all three to finish the job.\r\n" );
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document.write( "1/5 + (x-5)/x + y/5 = 1\r\n" );
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document.write( "That simplifies to\r\n" );
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document.write( "y = (25-x)/x \r\n" );
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document.write( "There is not enough information to give just \r\n" );
document.write( "one possible answer. There are many possible\r\n" );
document.write( "answers.  Here's why.\r\n" );
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document.write( "Suppose B is such a slow worker that it would \r\n" );
document.write( "take him a long time to do the whole job by \r\n" );
document.write( "himself (maybe it would even take him as long \r\n" );
document.write( "as 10 years!) So A and B would do virtually all \r\n" );
document.write( "the work.  B's contribution to the work effort\r\n" );
document.write( "of the A,B,C team is practically nothing.  So \r\n" );
document.write( "without B, the pair or workers A and C could \r\n" );
document.write( "virtually do the job in a tiny bit over 5 hours \r\n" );
document.write( "and finish at a tiny bit after 1:00PM.  \r\n" );
document.write( "It wouldn't matter about B resting, since he\r\n" );
document.write( "works so slow in this case.   \r\n" );
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document.write( "Now look at another extreme case.  Suppose B \r\n" );
document.write( "is the fast worker and it takes A and C ten \r\n" );
document.write( "years to do the job.   So it's practically the \r\n" );
document.write( "same as if B works 1/5th of the job in the\r\n" );
document.write( "hour from 8 till 9, rests for a half hour \r\n" );
document.write( "and does the remaining 4/5th of a job in 4 \r\n" );
document.write( "hours. He'd lose the half hour he rested, \r\n" );
document.write( "and finish at a little after 1:30PM.\r\n" );
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document.write( "Let's take an intermediate case, where A,B, and \r\n" );
document.write( "C all three work at the same rate. Then it would \r\n" );
document.write( "take each 3 times as long to do the job alone or \r\n" );
document.write( "3×5 or 15 hours each to do it alone.\r\n" );
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document.write( "So from 8:00AM till 9:00AM, they do 3 fifteenths\r\n" );
document.write( "or 3/15ths of the job.  Then in the 1/2 hour from \r\n" );
document.write( "9:00 till 9:30, they do \r\n" );
document.write( "(1/2)(2/15) = 1/15 of the job.  So that's a total \r\n" );
document.write( "of 4/15ths of the job at 9:30AM. They still have \r\n" );
document.write( "11/15ths of the job left to do, and since they can \r\n" );
document.write( "do 3/15ths in one hour it will take them \r\n" );
document.write( "(11/15)÷(3/15) or 11/3 or 3 2/3 hours to finish. \r\n" );
document.write( "That's 3 hours and 20 minutes after 9:30AM so \r\n" );
document.write( "they'll finish at 12:50AM.\r\n" );
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document.write( "So there are many possibiloities.  Check the problem \r\n" );
document.write( "again.  I'll bet something was left out. But don't\r\n" );
document.write( "go with the other tutor's solution.  \r\n" );
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document.write( "Edwin
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