Hi boomgoesthegmat,

In "work" questions, there are 2 common ways to get to the correct answer (although there are several different ways to "do the math"):

1) When there are 2 entities (people, machines, etc.) working on a task together, use the Work Formula.

2) Convert the individual rates of the 2 (or more) entities, combine and be sure to answer the question that's asked.

In this question, here's how you could use the two options mentioned:

We're told...

Machine A = 4 hours to complete an order

Machine B = 3 hours to complete the same order

We're asked how long it would take the two machines, WORKING TOGETHER, to complete the order.

1) Using the Work Formula: (A)(B)/(A+B).....

(4)(3)/(4+3) = 12/7 hours to complete the job

2) Using the individual rates:

Machine A:

4 hours to do the entire job --> 1 hour to do 1/4 of the job

Machine B:

3 hours to do the entire job --> 1 hour to do 1/3 of the job

In 1 hour, 1/4 + 1/3 = 7/12 of the job is done

**Note: this calculation tells you the FRACTION of the JOB that is complete in 1 HOUR**

Since there is 1 job to complete.....1/(7/12) = 12/7 hours to complete the job

Either way, the Final Answer is...

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Rich

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