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
It would take one machine 4 hours (OG16)
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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
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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Assume total work = 12 units (LCM of both the times)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
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