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It would take one machine 4 hours (OG16)

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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It would take one machine 4 hours (OG16)

Post Thu May 19, 2016 3:46 pm
It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

A) 7/12
B) 1 1/2
C) 1 5/7
D) 3 1/2
E) 7

OA: C

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OptimusPrep Master | Next Rank: 500 Posts
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Post Thu May 19, 2016 8:11 pm
boomgoesthegmat wrote:
It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

A) 7/12
B) 1 1/2
C) 1 5/7
D) 3 1/2
E) 7

OA: C
Assume total work = 12 units (LCM of both the times)
Work rate of machine 1 = 3 units/hr
Work rate of machine 2 = 4 units/hr

Total work = 12 units.
Total work rate when both machines work together = 7 units/hr

Hence the work would be completed in 12/7 hr = 1 5/7 hrs

Correct Option: C

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GMAT/MBA Expert

Post Thu May 19, 2016 4:41 pm
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...C

GMAT assassins aren't born, they're made,
Rich

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