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It would take one machine 4 hours to complete a large production order
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17 Dec 2012, 05:29

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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?

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16 Jun 2016, 05:06

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Walkabout 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

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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It would take one machine 4 hours to complete a large production order
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17 Dec 2012, 05:33

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Walkabout 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) \(\frac{7}{12}\)

(B) \(1 \frac{1}{2}\)

(C) \(1 \frac{5}{7}\)

(D) \(3 \frac{1}{2}\)

(E) 7

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.

Re: It would take one machine 4 hours to complete a large production order
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18 Jun 2013, 12:24

Bunuel wrote:

Walkabout 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

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 1/4+1/3=7/12 job per hour, which means that it takes 1/(7/12)=12/7 hours both machines to do the job.

Answer: C.

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?

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01 Aug 2016, 06:56

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Top Contributor

Walkabout 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

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

Re: It would take one machine 4 hours to complete a large production order
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31 Jan 2018, 20:18

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

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!
_________________

You've got what it takes, but it will take everything you've got

Re: It would take one machine 4 hours to complete a large production order
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20 Feb 2018, 11:08

Bunuel wrote:

Walkabout 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) \(\frac{7}{12}\)

(B) \(1 \frac{1}{2}\)

(C) \(1 \frac{5}{7}\)

(D) \(3 \frac{1}{2}\)

(E) 7

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.

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

It would take one machine 4 hours to complete a large production order
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20 Feb 2018, 11:40

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dave13 wrote:

Bunuel wrote:

Walkabout 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) \(\frac{7}{12}\)

(B) \(1 \frac{1}{2}\)

(C) \(1 \frac{5}{7}\)

(D) \(3 \frac{1}{2}\)

(E) 7

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.

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