It takes one machine 4 hours to complete a production order

Question

It takes one machine 4 hours to complete a 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 rates to complete the order?

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

Hey guys,

Was hoping to get a bit of help. I'm looking for some logic into the OG's answer explanation as to why you flip the fraction at the end. Any tips here would be great! question as follows:

so: 
Machine 1: 1/4 order in one hour
machine 2: 1/3 order in one hour

so together they can complete 7/12 of order in one hour.

(part i dont understand ==>) Therefore it takes (answer C) 12/7 hours (or 1 and 5/7 hours) for the two machines working together to complete the order.

Thanks to anyone who can help me with this (hopefully) very simple question!!

mbaiseasy · Answer

RT = W

Given:

R = 1/3 + 1/4 = 7/12
T = ?
W = 1

T = 1 / (7/12) = 12/7 = 1 5/7

Answer: C

Narenn · Answer

A bit different approach.

It takes one machine 4 hours to complete a production order :-  Machine A is completing 25% production order in one hour   \frac{100}{4} = 25

another machine 3 hours to complete the same order.  Machine B is completing 33.33% production order in one hour   \frac{100}{3} = 33.33

Both Machines together completing 25 + 33.33 = 58.33% production order in one hour

Both Machines working together would finish the total order in  \frac{100}{58.33} = 1.7 hours  or  1 \frac{5}{7}

Note :- We assume here total work to be 100% and then calculates how much % work is machine completing in one hour.

SVaidyaraman · Answer

Say the number of hours to complete a job is 2.5 o 5/2 hours
The amount of work completed in 1 hour is 1/2.5 = 2/5 th of the job

Or in other words if x/y th of the job is completed in 1 hour, the time taken to complete the job is y/x hours

EMPOWERgmatRichC · Answer

Hi All,

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

Benacher07 · Answer

4 hours to complete the task means that in 1 hours= 1/4 of the task
3 hours to complete the task means that in 1 hours= 1/3 of the task

1/4 +1/3 = 7/12
Since we want to know how much time it took : 12/7 hours = 7/7+5/7 = 1 5/7

Answer : C

jokschmer · Answer

in the ans it is not flip but convert in the form of rate = work / time and we are considering work as 1 so to make numerator 1 we have to push actual numerator along with denominator as we can write 7/12 is equals to 1/(12/7) and as per the formula of rate = work / time 12/7 denotes time... that question asked for....

ManifestDreamMBA · Answer

Direct formula, time = 3*4/(3+4) = 12/7
Answer C

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It takes one machine 4 hours to complete a production order

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It takes one machine 4 hours to complete a production order

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