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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OA 6
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Brent@GMATPrepNow
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One approach is to assign a "nice" value to the job.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?
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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.
So, the answer is 6
Cheers,
Brent
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Brent@GMATPrepNow
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Here's another approach . . .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?
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OA 6
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.
Answer = 6
Cheers,
Brent
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Brent@GMATPrepNow
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These kinds of questions are pretty tricky.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?
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
Brent Hanneson - Creator of GMATPrepNow.com
Thank you Brent. Your suggestions above have helped a lot.Brent@GMATPrepNow wrote:These kinds of questions are pretty tricky.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?
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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Jeff@TargetTestPrep
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We have a combined worker problem for which we can use the following formula: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?
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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
Answer: C
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