SOLUTION: 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. M

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.
Found 2 solutions by VFBundy, MathTherapy:
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
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

Portion of mail that Machine C sorts in 1/2 hour = 1/2 * 2/3 = 1/3

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.

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

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.

Percentage of job to be completed = Rate of work per hour * Hours worked

2/3 = 5/6 * Hours worked

2/3 * 6/5 = Hours worked

4/5 = Hours worked

So, working together, it takes Machine A and Machine B 4/5 hour...or 48 minutes...to complete the job.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

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.

Machine A does job in 2 hours, or of job in 1 hour Machine B does job in 3 hours, or of job in 1 hour Machine C does job in hours, or of job in 1 hour With machine C working for hour, and with T being the time machines A & B take to finish the job, we get: 2 + 3T + 2T = 6 ------- Multiplying by LCD, 6 3T + 2T = 6 - 2 5T = 4 Time machines A and B took to complete job, or

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