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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

If ‘A’ can complete a task in 3 hours and ‘B’ can complete [#permalink]
08 Mar 2010, 02:00

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

76% (01:25) correct
24% (00:15) wrong based on 37 sessions

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

Last edited by walker on 08 Mar 2010, 05:08, edited 1 time in total.

Re: Facing problem with this question...... [#permalink]
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]
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]
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]
09 Mar 2010, 01:43

2

This post received KUDOS

Expert's post

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]
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]
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]
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]
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

Re: Facing problem with this question...... [#permalink]
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]
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)

This week went in reviewing all the topics that I have covered in my previous study session. I reviewed all the notes that I have made and started reviewing the Quant...

I was checking my phone all day. I wasn’t sure when I would receive the admission decision from Tepper. I received an acceptance from Goizueta in the early morning...

I started running as a cross country team member since highshcool and what’s really awesome about running is that...you never get bored of it! I participated in...