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## machines R and S

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 2 member replies
josh80 Senior | Next Rank: 100 Posts
Joined
03 Nov 2013
Posted:
72 messages
1

#### machines R and S

Sun Dec 15, 2013 3:26 pm
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

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12

OA 6

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Brent@GMATPrepNow GMAT Instructor
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Sun Dec 15, 2013 3:49 pm
josh80 wrote:
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

3
4
6
9
12

OA 6
One approach is to assign a "nice" value to the job.
Say, the job is to make 36 widgets.

R does a certain job in 36 hours
This means that machine R's rate is 1 widget/hour

S does the job in 18 hours
This means that machine S's rate is 2 widgets/hour

So, their combined rate is 3 widgets/hour.

The question asks us to complete the job in 2 hours.
To make 36 widgets in 2 hours, the combined rate of the two machines must be 18 widgets/per hour.
If the combined rate (of 1 R machine and 1 S machine) is 3 widgets/hour, then we'd need 6 of each machine to reach a rate of 18 widgets/hour.

Cheers,
Brent

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Brent@GMATPrepNow GMAT Instructor
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Sun Dec 15, 2013 3:50 pm
josh80 wrote:
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

3
4
6
9
12

OA 6
Here's another approach . . .

When it comes to questions where we must complete an entire job, I often (not always) like to know what can be accomplished in 1 unit of time (in this case, 1 hour).

Machine R can complete 1/36 of the job in 1 hour.
Machine S can complete 1/18 of the job in 1 hour.
Since 1/36 + 1/18 = 1/12, we know that, combined, machines R and S can complete 1/12 of the job in 1 hour.

From here we can apply some logic.
If 1/12 of the job is completed in 1 hour (with 1 R machine and 1 S machine), then we could complete the entire job in 1 hour if we had 12 of each machine type.
However, the question asks us to find the # of machines required to complete the job in 2 hours. So, we need half as many machines. In other words, we need 6 of each machine.

Cheers,
Brent

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josh80 Senior | Next Rank: 100 Posts
Joined
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Posted:
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Mon Dec 16, 2013 12:56 pm
Thank you for the solutions Brent. I always seems to struggle with Rate & Work questions. Do you have any suggestions on how to overcome this conceptually?

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Brent@GMATPrepNow GMAT Instructor
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Mon Dec 16, 2013 1:02 pm
josh80 wrote:
Thank you for the solutions Brent. I always seems to struggle with Rate & Work questions. Do you have any suggestions on how to overcome this conceptually?
These kinds of questions are pretty tricky.
In my opinion, the two tips I gave are the most important:

1) For questions in which we must complete an entire job, it's often useful to determine what can be accomplished in 1 unit of time (1 hour, 1 day, etc).

2) You should also consider assigning a "nice" value to the job. For example, you may say that an entire job consists of making 48 widgets.

You should also keep the following rules in your back pocket:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

I hope that helps.

Cheers,
Brent

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josh80 Senior | Next Rank: 100 Posts
Joined
03 Nov 2013
Posted:
72 messages
1
Fri Dec 20, 2013 11:51 am
Brent@GMATPrepNow wrote:
josh80 wrote:
Thank you for the solutions Brent. I always seems to struggle with Rate & Work questions. Do you have any suggestions on how to overcome this conceptually?
These kinds of questions are pretty tricky.
In my opinion, the two tips I gave are the most important:

1) For questions in which we must complete an entire job, it's often useful to determine what can be accomplished in 1 unit of time (1 hour, 1 day, etc).

2) You should also consider assigning a "nice" value to the job. For example, you may say that an entire job consists of making 48 widgets.

You should also keep the following rules in your back pocket:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

I hope that helps.

Cheers,
Brent
Thank you Brent. Your suggestions above have helped a lot.

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Jeff@TargetTestPrep GMAT Instructor
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Thu Dec 07, 2017 6:32 am
josh80 wrote:
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

3
4
6
9
12
We have a combined worker problem for which we can use the following formula:

work (1 machine) + work (2 machine) = total work completed

Since we are completing one job, we can say:

work (1 machine) + work (2 machine) = 1

We are given that a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours.

Thus, the rates for the two machines are as follows:

rate of machine R = 1/36

rate of machine S = 1/18

We are also given that the company used the same number of each type of machine to do the job in 2 hours. If we let x = the number of each machine used, we can multiply each rate by x and we have:

rate of x number of R machines = x/36

rate of x number of S machines = x/18

Finally, since we know some number of R and S machines worked for two hours, and since work = rate x time, we can calculate the work done by each type of machine.

work done by x number of R machines = 2x/36 = x/18

work done by x number of S machines = 2x/18 = x/9

Now we can determine x using the combined worker formula:

work (machine R) + work (machine S) = 1

x/18 + x/9 = 1

x/18 + 2x/18 = 1

3x/18 = 1

x/6 = 1

x = 6

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