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RATE - MACHINES X & y

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RATE - MACHINES X & y

by pappueshwar » Tue Mar 20, 2012 10:04 am

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Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

18
13+1/2
7+1/5
4+1/2
3+2/3

OA IS A
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by Mike@Magoosh » Tue Mar 20, 2012 10:17 am
Hi, there. I'm happy to help with this. :)

BIG IDEA: when machines work together, you add rates.

Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours.

So, the rate of X, which I'll call RX = (1 job)/(9 hours) = 1/9

Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours.

(amount of work) = (rate of work)*(time)

The amount of work X did was (1/9)*(3) = 1/3 of a job.

The two machines worked at a combined rate (RX + RY) for 4 hours, and completed the last 2/3 of the job. (Notice, we find the combined rate by adding the individual rates.)

2/3 = 4*(RX + RY)
1/6 = RX + RY
1/6 = 1/9 + RY
RY = 1/6 - 1/9 = 3/18-2/18 = 1/18

The rate of Y is RY = 1/18, which means Y, working alone, would complete one job in 18 hours.
Answer = A

Here's another work question involving combining rates for practice:
https://gmat.magoosh.com/questions/73
After you submit your answer, the next page will have the video explanation.

Does all this make sense? Let me know if you have any questions.

Mike :)
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by pappueshwar » Tue Mar 20, 2012 10:27 am
thanks
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by GMATGuruNY » Tue Mar 20, 2012 11:37 am
pappueshwar wrote:Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

18
13+1/2
7+1/5
4+1/2
3+2/3

OA IS A
Let the job = 36 units (the LCM of 9, 3 and 4).
Rate for X alone = w/t = 36/9 = 4 units per hour.
Work completed by X in 3 hours = r*t = 4*3 = 12 units.
Remaining work = 36-12 = 24 units.
Combined rate for X+Y to finish the job = w/t = 24/4 = 6 units per hour.
Thus, rate for Y alone = rate for X+Y - rate for X alone = 6-4 = 2 units per hour.
Time for Y to complete the job alone = w/r = 36/2 = 18 hours.

The correct answer is A.
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by Mochad » Tue Mar 20, 2012 2:02 pm
Hi, What is the level of difficulty of this exercise? Additionally, I was not able to solve the problem from the first attempt! And it took me 3:10 in the second? Should I pace my self even faster? Like to solve it in 2 mins?
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by bx » Wed Mar 21, 2012 4:32 am
pappueshwar wrote:Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

18
13+1/2
7+1/5
4+1/2
3+2/3

OA IS A
rate of work done per unit of time:
(1 job)/(9 hours) for machine X and (1 job)/(y hours) for machine Y

to complete 1 job:
(3 hours)*(1 job)/(9 hours) + (4 hours)*( (1 job)/(9 hours) + (1 job)/(y hours) ) = (1 job)

solve for (y hours)

Ans [spoiler](A)[/spoiler]
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by ronnie1985 » Wed Mar 21, 2012 9:23 am
Machine X did 1/3 of job and 2/3 job was done together in 4 hours, rate together = 2/(3*4). Rate of X = 1/9. Therefore rate of Y = 1/6-1/9 = 1/18. Therefore Y alone can do the job in 18 hours.
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by Mike@Magoosh » Wed Mar 21, 2012 10:24 am
Mochad wrote:Hi, What is the level of difficulty of this exercise? Additionally, I was not able to solve the problem from the first attempt! And it took me 3:10 in the second? Should I pace my self even faster? Like to solve it in 2 mins?
I would say this problem is in the easy to medium range, in terms of difficulty, say in a low 600s range. There are definitely many more complicated math problems on the GMAT.

Yes, you definitely should be striving to solve problems like this at a faster rate, something under 2:00 per question.

You might consider looking at Magoosh test prep. We have 200+ lesson videos explaining all the content and strategy you need for the GMAT, including a video explaining how to handle work problems like this. We have over 800 practice problems, each with its own video explanation. In my post above, I gave the link to one example work question. Here's another:
https://gmat.magoosh.com/questions/53
After you submit your answer, the next page will have the video explanation.

Working with Magoosh will give you the mastery you need and, especially with the time-saving strategies, will help you work with the required efficiency on questions like these.

Let me know if you have any questions.

Mike :)
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by [email protected] » Wed Mar 21, 2012 4:48 pm
Yes this question is a type of question wherein it should take a lot of time.

got it in a 2 : 06 mins...
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
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by Mochad » Thu Mar 22, 2012 3:23 am
Thanks Mike@Magoosh. I checked the link you gave me (question 53), it was amazing! Unfortunately, I have set up my studying plan including the studying resources! And I don't like going back and changing ;) BTW, your marketing plan is excellent :D


Good job [email protected]! Wish good luck :)
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by Whitney Garner » Thu Mar 22, 2012 7:19 am
Mochad wrote:Hi, What is the level of difficulty of this exercise? Additionally, I was not able to solve the problem from the first attempt! And it took me 3:10 in the second? Should I pace my self even faster? Like to solve it in 2 mins?
Hi Mochad!

I'm actually not overly concerned that this question took you over 2 minutes (but I would want to get the time under 3). It is a word problem, and a combine work problem (with multiple steps), so something of this nature would take longer to read, understand, interpret, plan, and then inevitably solve.

Remember that its a 2 minute per question AVERAGE. There will be questions that take longer, and others that you can finish quickly. I know that in the OG12th alone, there are TONS of problems with high Q#s (meaning relatively more difficult) that are straightforward algebra or simplification, and will likely take only 1 minute if you know the algebra/exponent/fraction rules.

My recommendation is that you keep track of problem types and try to identify those that take you well over 2 minutes (over 3) and focus on getting those down under 3, then take a look at the problem types that you are able to complete in UNDER 2 (accurately of course), and see if there is balance. On test day there will CERTAINLY be questions that take me close to 3 minutes (or maybe even a bit longer), but I can feel okay because I have enough "quick" questions to make up for it!

Good Luck with your Studies!!
:)
Whit
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by killer1387 » Thu Mar 22, 2012 7:38 am
pappueshwar wrote:Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

18
13+1/2
7+1/5
4+1/2
3+2/3

OA IS A
2/3 =(1/x+1/9)*4
=> 1/x=1/6-1/9=3/54=1/18

x=18
HENCE A
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by Mochad » Thu Mar 22, 2012 8:20 am
Hi Whit :)

Thanks a lot for your reply :D It calmed me down as I was concerned with the timing problem taking into consideration its importance during the actual test! I guess time management is a forth section being test by GMAC!
Whitney Garner wrote:I'm actually not overly concerned that this question took you over 2 minutes (but I would want to get the time under 3). It is a word problem, and a combine work problem (with multiple steps), so something of this nature would take longer to read, understand, interpret, plan, and then inevitably solve.
That is what I want to hear :D :D :D
Whitney Garner wrote:Remember that its a 2 minute per question AVERAGE. There will be questions that take longer, and others that you can finish quickly. I know that in the OG12th alone, there are TONS of problems with high Q#s (meaning relatively more difficult) that are straightforward algebra or simplification, and will likely take only 1 minute if you know the algebra/exponent/fraction rules.
RATIONAL ANSWER! Thank you again :) I was thinking about something similar! But couldn't answer as I'm not an expert nor have the experience :(
Whitney Garner wrote:My recommendation is that you keep track of problem types and try to identify those that take you well over 2 minutes (over 3) and focus on getting those down under 3, then take a look at the problem types that you are able to complete in UNDER 2 (accurately of course), and see if there is balance. On test day there will CERTAINLY be questions that take me close to 3 minutes (or maybe even a bit longer), but I can feel okay because I have enough "quick" questions to make up for it!
mmm that is interesting! I'm aware that half of the Math Q I'm going to encounter are PS and the other half is DS, but how can I know if there is a balance if I don't know the number of, let us say, algebra questions?
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Re: RATE - MACHINES X & y

by Brent@GMATPrepNow » Tue Apr 07, 2020 9:47 am
pappueshwar wrote: ↑
Tue Mar 20, 2012 10:04 am
 Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

18
13+1/2
7+1/5
4+1/2
3+2/3

OA IS A

Another way to solve this question is to assign a nice value to the job.
So, we want to use a value that works well with the given numbers in the question (9, 3 and 4 hours).
Since 36 is the least common multiple of 9, 3 and 4, let's say the entire job consists of making 36 widgets

Machine X can complete a certain job in 9 hours
So, Machine X's RATE = 36/9 = 4 widgets per hour

Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours.
At its rate of 4 widgets per hour, Machine X would have produced 12 widgets in 3 hours
36 - 12 = 24
So, after the first 3 hours, the two machines would need to produce the 24 remaining widgets in the job

Since the two machines COMBINED produced the remaining 24 in 4 hours, their COMBINED RATE = 24/4 = 6 widgets per hour

We can write: (Machine X's rate) + (Machine Y's rate) = 6 widgets per hour
Substitute to get: 4 + (Machine Y's rate) = 6 widgets per hour
From this, we can see that Machine Y's rate = 2 widgets per hour

How many hours would it have taken machine Y, working alone, to complete the entire job?
time = output/rate
So, time = 36/2 = 18

Answer: A

Cheers,
Brent
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