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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) \(\frac{7}{12}\)
(B) \(1 \frac{1}{2}\)
(C) \(1 \frac{5}{7}\)
(D) \(3 \frac{1}{2}\)
(E) 7
(A) \(\frac{7}{12}\)
(B) \(1 \frac{1}{2}\)
(C) \(1 \frac{5}{7}\)
(D) \(3 \frac{1}{2}\)
(E) 7
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Walkabout
The rate of the first machine is 1/4 job per hour;
The rate of the second machine is 1/3 job per hour;
Thus, the combined rate of the machines is \(\frac{1}{4}+\frac{1}{3}=\frac{7}{12}\) job per hour, which means that it takes \(\frac{1}{(\frac{7}{12})}=\frac{12}{7}=1 \frac{5}{7}\) hours both machines to do the job.
Answer: C.
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JeffTargetTestPrep
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Expert reply
Posts: 2,973
Walkabout
We can classify this problem as a “combined worker” problem. To solve this type of problem we should use the formula:
Work (done by worker 1) + Work (done by worker 2) = Total Work Completed
It takes machine one 4 hours to complete a job, so the rate of machine one is ¼. It takes machine two 3 hours to complete a job, so the rate of machine two is 1/3. Since we know they are both working together to complete the job, we can label this unknown time as “t” for each machine during the time that both machines are working together. Since rate x time = work, we can multiply to get the work completed for each machine.
Finally, we can plug our two work values into the combined work formula and determine t. Since the job is completed, the total work completed is 1.
Work (done by worker 1) + Work (done by worker 2) = Total Work Completed
(1/4)t + (1/3)t = 1
Multiplying the entire equation by 12 gives us:
3t + 4t = 12
7t = 12
t = 12/7 = 1 5/7
Answer is C.
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General Discussion
Bunuel
Suppose we change the wording of the problem to "It would take 2 machines 4 hours together to complete a large production" How would you solve for that ? I'm trying to better understand the nature of the problem. Thanks. My logic says the rate is still the same since it still is 4 hours. If so than what does it change?
Posts: 1
how can the answer be C
in options dere is no option of 12/7
in options dere is no option of 12/7
blueseas
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arpana10july
there is a typo in choice.
machine A takes 4 hr
machine B takes 3 hr
then together they will take = product /sum =\((4*3)/(4+3)\)
Posts: 13
arpana10july
12/7 is equivalent to 1 and 5/7
Posts: 6,727
Updated on: 02 Apr 2020, 06:56
Originally posted by BrentGMATPrepNow on 01 Aug 2016, 06:56.
Last edited by BrentGMATPrepNow on 02 Apr 2020, 06:56, edited 1 time in total.
Last edited by BrentGMATPrepNow on 02 Apr 2020, 06:56, edited 1 time in total.
Walkabout
Another approach is to assign the ENTIRE job a certain number of units.
The least common multiple of 4 and 3 is 12.
So, let's say the ENTIRE production order consists of 12 widgets.
It would take one machine 4 hours to complete a large production...
Rate = output/time
So, this machine's rate = 12/4 = 3 widgets per hour
...and another machine 3 hours to complete the same order.
Rate = units/time
So, this machine's rate = 12/3 = 4 widgets per hour
So, their COMBINED rate = 3 + 4 = 7 widgets per hour.
Working simultaneously at their respective constant rates, to complete the order?
Time = output/rate
= 12/7 hours
Answer:
JeffTargetTestPrep Bunuel
When we are given t as 3 and 4 hours why are we still assigning an unknown variable?
When we are given t as 3 and 4 hours why are we still assigning an unknown variable?
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Expert reply
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...
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...
GMAT assassins aren't born, they're made,
Rich
adkikani
Hi adkikani
The reason we are assigning t(an unknown variable) for time, because we don't
know how much time will be take to complete the entire work, when working together.
When we are given 3 and 4 hours as time, it means that the individual machines
will complete the entire work(working alone) in 3 and 4 hours respectively.
Alternate approach
Since it takes one machine 4 hours to complete the order and the second machine takes
3 hours to complete the order, we can assume the work done to be 60 units.
The individual rate of the first machine to complete the work will be 15 units/hour
and the rate of the second machine is 20 units/hour. So, together they will complete 35 units in an hour.
Therefore, the time taken for both the machines(combined) is \(\frac{60}{35} = \frac{12}{7} =1\frac{5}{7}\)(Option C)
Hope that helps!
Bunuel
Hi Bunuel
can you help to understand the logic behind this \(\frac{1}{(\frac{7}{12})}=\frac{12}{7}=1 \\\\
why do you flip \frac{7}{12}\) in order to know how much time will it take both to complete
dave13
Hi dave13
Basically, If \(\frac{1}{x}\) of the work takes place in 1 hour, the time taken to complete the work will be x!
Here in this question, x = \(\frac{7}{12}\)
So, when we finish \(\frac{1}{(\frac{7}{12})}\) of the work in 1 hour, the time taken to complete the work is \(\frac{12}{7}\)
Hope that helps you!
Ta=4hrs, Tb=3hrs
Ra=1/Ta =1/4 and Rb=1/Tb=1/3
Rate when the two machines work together, Rab, can be gotten as follows:
1/Rab =1/Ra + 1/Rb = 1/4+1/3 = 7/12
But Tab=1/Rab = 12/7 hrs
Posted from my mobile device
Ra=1/Ta =1/4 and Rb=1/Tb=1/3
Rate when the two machines work together, Rab, can be gotten as follows:
1/Rab =1/Ra + 1/Rb = 1/4+1/3 = 7/12
But Tab=1/Rab = 12/7 hrs
Posted from my mobile device
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dave13
dave13
can you help to understand the logic behind this \(\frac{1}{(\frac{7}{12})}=\frac{12}{7}=1 \\In \(\frac{7}{12}\) the unit is \(\frac{job}{hour}\). You need hour (time). So, just flip it. You'll get the hour.
Thanks__
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Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
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Quote:
Hello all,
We can solve this question logically that will save your time for sure!
Choice D and E:
One machine (x) takes 3 hrs to complete whole the job and another machine (y) takes 4 hrs to complete the same job. If if they do the same job simultaneously, then their total time will be less than 3 hours. So, the answer choices (D,E) which keeps more than 3 hours are crossed out.
In real life example:
You do a job by 3 hrs; i do the same job by 4 hrs. If i help you to do the SAME job (with respective constant rate), you will need LESS THAN 3 hours to complete whole the job.
Choice A, B and C:
Suppose, x takes 3 hours to take the job; and y takes 3 hours to take the same job (with respective constant rate). If they do simultaneously, then they need \(1\frac{1}{2}\) hours to complete whole the job, right? But, in the question prompt, y takes 4 hours (who is slower than x). So, they need more than \(1\frac{1}{2}\) hours if they do simultaneously. So, A and B are out. The correct choice is C.
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EMPOWERgmatRichC
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Expert reply
Asad
Hi Asad,
That is a great series of deductions - and it shows how GMAT questions can almost always be approached in more than one way.
GMAT assassins aren't born, they're made,
Rich
Let's assume that the production order is 1 unit in size.
Machine 1 can complete 1/4 of the order in 1 hour, while Machine 2 can complete 1/3 of the order in 1 hour. Working together, they will complete 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of the order in 1 hour.
Therefore, we can set up the equation:
(7/12) * t = 1
where "t" is the time it takes both machines working together to complete the order.
Solving for "t", we get:
t = 12/7 hours
Therefore, the answer is approximately 1.71 hours or 1 hour and 42 minutes, and the correct choice is (C) 1 5/7.
Machine 1 can complete 1/4 of the order in 1 hour, while Machine 2 can complete 1/3 of the order in 1 hour. Working together, they will complete 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of the order in 1 hour.
Therefore, we can set up the equation:
(7/12) * t = 1
where "t" is the time it takes both machines working together to complete the order.
Solving for "t", we get:
t = 12/7 hours
Therefore, the answer is approximately 1.71 hours or 1 hour and 42 minutes, and the correct choice is (C) 1 5/7.
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