Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
If ‘A’ can complete a task in 3 hours and ‘B’ can complete
[#permalink]
Show Tags
Updated on: 08 Mar 2010, 05:08
1
00:00
A
B
C
D
E
Difficulty:
(N/A)
Question Stats:
88% (00:32) correct 12% (00:15) wrong based on 113 sessions
HideShow timer Statistics
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?
This is a problem of Arithmetic, related to work and time. It is a very interesting problem but I am unable to solve it. I am still trying to solve it, I am thinking that it took (3 + 6) / 2 = 4.5, mean of the time taken by the two. But, my answer is wrong.
Please explain the logic.
Thanks
Originally posted by david01 on 08 Mar 2010, 02:00.
Last edited by walker on 08 Mar 2010, 05:08, edited 1 time in total.
Re: Facing problem with this question......
[#permalink]
Show Tags
09 Mar 2010, 01:43
5
nickk wrote:
I haven't seen anyone post the formula so I'll go ahead and do it
1/T = 1/A + 1/B + .... 1/N
so if you have N entities which can do the same job in different amounts of time (denoted by A, B, ..., N above), the total amount of time it takes them to do the same tas working together is T.
I think you can solve all similar problems using this formula.
The above is correct and it's good to memorize cases for two and three entities (workers, pumps, ...):
General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:
Given that \(a\) and \(b\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{a*b}{a+b}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{a}+\frac{1}{b}=\frac{1}{t}\)).
General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:
\(T_{(A&B&C)}=\frac{a*b*c}{ab+ac+bc}\) hours.
Also for rate problems it's good to know that:
TIME to complete one job=Reciprocal of rate. eg 6 hours needed to complete one job (time) --> 1/6 of the job done in 1 hour (rate).
Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.
Re: Facing problem with this question......
[#permalink]
Show Tags
08 Mar 2010, 07:17
david01 wrote:
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?
This is a problem of Arithmetic, related to work and time. It is a very interesting problem but I am unable to solve it. I am still trying to solve it, I am thinking that it took (3 + 6) / 2 = 4.5, mean of the time taken by the two. But, my answer is wrong.
Please explain the logic. Thanks
A do 1/3 task in 1 hour B do 1/6 task in 1 hour
A & B together do 1/3 + 1/6 = 1/2 task in 1 hour. So they complete task in 2 hours.
Re: Facing problem with this question......
[#permalink]
Show Tags
08 Mar 2010, 07:19
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?
A can complete task in 3 hours. In 1 hour A can complete 1/3 of the work. B can complete task in 6 hours. In 1 hour B can complete 1/6 of the work.
Both together can complete how much work in an hour = 1/3 + 1/6 = 3/6 = 1/2
So 1/2 work can be completed in 1 hour by A and B together. How much time it takes to complete the work = 2/1 hours = 2 hours.
Re: Facing problem with this question......
[#permalink]
Show Tags
08 Mar 2010, 12:06
I haven't seen anyone post the formula so I'll go ahead and do it
1/T = 1/A + 1/B + .... 1/N
so if you have N entities which can do the same job in different amounts of time (denoted by A, B, ..., N above), the total amount of time it takes them to do the same tas working together is T.
I think you can solve all similar problems using this formula.
Re: Facing problem with this question......
[#permalink]
Show Tags
09 Mar 2010, 01:55
david01 wrote:
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?
This is a problem of Arithmetic, related to work and time. It is a very interesting problem but I am unable to solve it. I am still trying to solve it, I am thinking that it took (3 + 6) / 2 = 4.5, mean of the time taken by the two. But, my answer is wrong.
Please explain the logic.
Thanks
Let task be writing 18 pages (multiple of 3 and 6)\
A writes 18/3 = 6 pages an hour B write 18/6 = 3 pages per hour
Both write 9 pages per hour So total time required is 18/9=2 hours while working together...
Hope this helps you in solving such problems without working with x, y fractions.
_________________
Re: Facing problem with this question......
[#permalink]
Show Tags
13 Mar 2010, 10:22
Bunuel wrote:
nickk wrote:
I haven't seen anyone post the formula so I'll go ahead and do it
1/T = 1/A + 1/B + .... 1/N
so if you have N entities which can do the same job in different amounts of time (denoted by A, B, ..., N above), the total amount of time it takes them to do the same tas working together is T.
I think you can solve all similar problems using this formula.
The above is correct and it's good to memorize cases for two and three entities (workers, pumps, ...):
General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:
Given that \(a\) and \(b\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{a*b}{a+b}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{a}+\frac{1}{b}=\frac{1}{t}\)).
General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:
\(T_{(A&B&C)}=\frac{a*b*c}{ab+ac+bc}\) hours.
Also for rate problems it's good to know that:
TIME to complete one job=Reciprocal of rate. eg 6 hours needed to complete one job (time) --> 1/6 of the job done in 1 hour (rate).
Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.
Time*Rate=Distance Time*Rate=Job
Hope it helps.
Kudos Bunuel!!
Well, in some cases there are multiple persons doing the same job. e.g 5 men doing a job in 6 hours, while 9 women doing the same job in 6 hours & 10 boys doing the same job in 8 hours.
What's the formula for such cases?
_________________
Re: Facing problem with this question......
[#permalink]
Show Tags
06 Jan 2012, 05:12
Hussain15 wrote:
Well, in some cases there are multiple persons doing the same job. e.g 5 men doing a job in 6 hours, while 9 women doing the same job in 6 hours & 10 boys doing the same job in 8 hours. What's the formula for such cases?
Even I would be interested to know if there exists a formula for such problems. I am unusually weak in such work-rate problems and I struggle frequently. Any help would be appreciated.
_________________
Re: Facing problem with this question......
[#permalink]
Show Tags
06 Jan 2012, 20:05
This is a unit rate problem.
RULE: 1. When you are given something like, something takes x hours to complete, then the rate is 1/x 2.When working together, the rates add.
Here, A's rate is 1/3, B's rate is 1/6
So, working together, A + B = 1/3 + 1/6 = 3/6 = 1/2
Now inverse again to find the number of hours (since unit rate) = 2 hours
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 172
Location: Kuwait
Schools: Columbia university
Re: Facing problem with this question......
[#permalink]
Show Tags
07 Jan 2012, 11:26
here is the easiest approach.
A can complete 1/3 of the task in one hour, while B can complete 1/6 of the task is one hour. the formula to use is as following to get how much can they both achieve in one hour:
1/3+1/6=1/x
common denominator====>6
2/6+1/6=3/6 after simplification becomes 1/2
so both of them can finish the one half of the task in one hour, and in order to get the number of hours for the whole task just reverse the fraction, which will be 2
Re: Facing problem with this question......
[#permalink]
Show Tags
10 Sep 2012, 06:56
Though this was posted long ago, the questions raised by Hussain and Siddrat are quite good.I also need Bunuel here. But, my take on Hussain's question is: if m, w and b represent the times a man, a woman and a boy take in that order. I think we could get the rate for a single person of each category: 1/( No. of worker * Time for all workers) Thus, the rates for a single person: man=1/(5*6) , woman =1/(9*6), boy=1/(10*8)
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete
[#permalink]
Show Tags
30 Dec 2018, 08:06
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
88% (00:32) correct 
