Question 1168449
Rate it takes Machine A sorts the mail = 1/2 mail per hour
Rate it takes Machine B sorts the mail = 1/3 mail per hour
Rate it takes Machine C sorts the mail = 2/3 mail per hour
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Portion of mail that Machine C sorts in 1/2 hour = 1/2 * 2/3 = 1/3
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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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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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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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Percentage of job to be completed = Rate of work per hour * Hours worked
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2/3 = 5/6 * Hours worked
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2/3 * 6/5 = Hours worked
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4/5 = Hours worked
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<b>So, working together, it takes Machine A and Machine B 4/5 hour...or 48 minutes...to complete the job.</b>