document.write( "Question 1168449: The local post office has three machines for sorting the mail. If each works alone, machine A can accomplish the job in 2 hours, machine B in 3hours and machine C in 1 1/2 hours. Machine C begins the job and works for half an hour when it suddenly breaks down. Machine A and B are then activated and work together to complete the sorting process. How long does it take for machines A and B to finish. \n" ); document.write( "

Algebra.Com's Answer #793421 by VFBundy(438) $\"\"$ $\"About$

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Rate it takes Machine A sorts the mail = 1/2 mail per hour
\n" ); document.write( "Rate it takes Machine B sorts the mail = 1/3 mail per hour
\n" ); document.write( "Rate it takes Machine C sorts the mail = 2/3 mail per hour
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\n" ); document.write( "Portion of mail that Machine C sorts in 1/2 hour = 1/2 * 2/3 = 1/3
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\n" ); document.write( "At the point Machine C breaks down, it has sorted 1/3 of the mail, meaning there is 2/3 mail left to be sorted.
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\n" ); document.write( "Rate it takes Machine A and Machine B to sort mail working together = (1/2 + 1/3) mail per hour = 5/6 mail per hour
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\n" ); document.write( "So, we know that Machine A and Machine B can sort 5/6 of the mail per hour, and there is 2/3 of the mail left to be sorted.
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\n" ); document.write( "Percentage of job to be completed = Rate of work per hour * Hours worked
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\n" ); document.write( "2/3 = 5/6 * Hours worked
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\n" ); document.write( "2/3 * 6/5 = Hours worked
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\n" ); document.write( "4/5 = Hours worked
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\n" ); document.write( "So, working together, it takes Machine A and Machine B 4/5 hour...or 48 minutes...to complete the job. \n" ); document.write( "

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