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If ‘A’ can complete a task in 3 hours and ‘B’ can complete

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

[Reveal] Spoiler:
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.
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Re: Facing problem with this question...... [#permalink] New post 09 Mar 2010, 01:43
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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.
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Re: Facing problem with this question...... [#permalink] New post 08 Mar 2010, 07:08
I made tables. I hope this is right or I did a bunch of work for no reason. I picked the work to be traveling a distance of 12 miles

[list=]Separate
A B
R 4 mph 2 mph
T 3 hrs 6 hrs
D 12 mi 12 mi

Together
A B Together
R 4 mph 2 mph
T t t t
D 12-d d 12 mi


4t=12-d and 2t=d
t=3-d/4
so
2(3-d/4)=d
6-.5d=d
6=1.5d
d=4
so
Together with d set to 4
A B Together
R 4 mph 2 mph
T t t t
D 8 mi 4 mi 12 mi

4t=8
so
t=2 hrs
[/list]
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Last edited by vannbj on 08 Mar 2010, 07:20, edited 1 time in total.
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Re: Facing problem with this question...... [#permalink] New post 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.
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Re: Facing problem with this question...... [#permalink] New post 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.

Hope it is clear.
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Re: Facing problem with this question...... [#permalink] New post 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.
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Re: Facing problem with this question...... [#permalink] New post 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.
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Re: Facing problem with this question...... [#permalink] New post 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?
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Re: Facing problem with this question...... [#permalink] New post 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.
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Re: Facing problem with this question...... [#permalink] New post 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
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Re: Facing problem with this question...... [#permalink] New post 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

hope this helps
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Re: Facing problem with this question...... [#permalink] New post 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)
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Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete [#permalink] New post 13 Nov 2012, 22:00
\frac{1}{6}+\frac{1}{3}=\frac{1}{x}

\frac{1}{x}=\frac{1}{2}

Answer: time = reciprocal of rate = 2 hours
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Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete   [#permalink] 13 Nov 2012, 22:00
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