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Work and rate problem

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Director
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Joined: 02 Sep 2016
Posts: 786
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Work and rate problem [#permalink]

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New post 15 Aug 2017, 22:30
Hello BrushMyQuant, abhimahna, and Bunuel

If we are given that A can do a work in 12 hours and B can do the same work in 18 hours. A started the work and B joined him after 6 hours. How much time will they both take to complete the work?


Let total work = 36
A can do 3 units per hour
B can do 2 units per hour

Together they finish 5 units per hour


A started the work and worked alone for 6 hours. Therefore A finished 18 units of work.

Amount of work left= 36-18= 18

I am confused about the steps from here.

What I dis was, I found new units per hour for both A and B

A= 3/2 UNITS/HOUR
B= 1 UNIT/HOUR

AND got the answer 36/5 which is incorrect.

What is the error in the above method?
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Work and rate problem [#permalink]

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New post 15 Aug 2017, 22:42
Shiv2016 wrote:
I am confused about the steps from here.

What I dis was, I found new units per hour for both A and B

A= 3/2 UNITS/HOUR
B= 1 UNIT/HOUR

AND got the answer 36/5 which is incorrect.


What is the error in the above method?


Hi Shiv2016 ,

The steps highlighted above are incorrect.

Why are you calculating the new unit of work? I mean you cannot say that the efficiency of A and B would change when the work left is less.

As per your method, you found that both A and B are doing the work at 5 units/hour.

Work left when B joined = 18 units.

If they are doing at the rate of 5 units per hour, total time taken to complete the whole work = 18/5 = 3 hours and 36 mins.

Does that make sense?
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Director
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Joined: 02 Sep 2016
Posts: 786
Premium Member CAT Tests
Re: Work and rate problem [#permalink]

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New post 15 Aug 2017, 23:03
abhimahna wrote:
Shiv2016 wrote:
I am confused about the steps from here.

What I dis was, I found new units per hour for both A and B

A= 3/2 UNITS/HOUR
B= 1 UNIT/HOUR

AND got the answer 36/5 which is incorrect.


What is the error in the above method?


Hi Shiv2016 ,

The steps highlighted above are incorrect.

Why are you calculating the new unit of work? I mean you cannot say that the efficiency of A and B would change when the work left is less.

As per your method, you found that both A and B are doing the work at 5 units/hour.

Work left when B joined = 18 units.

If they are doing at the rate of 5 units per hour, total time taken to complete the whole work = 18/5 = 3 hours and 36 mins.

Does that make sense?



abhimahna thank you for your reply.

When we find their efficiency for completing the work, we find it according to the amount of work given. Won't it change when the amount of work will change?
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Re: Work and rate problem [#permalink]

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New post 15 Aug 2017, 23:12
Shiv2016 wrote:
abhimahna thank you for your reply.

When we find their efficiency for completing the work, we find it according to the amount of work given. Won't it change when the amount of work will change?


Hi Shiv2016 ,

Again the highlighted line is incorrect.

When we are given A can complete a work in 12 hours, his efficiency will remain the same no matter how much work is left unless you are told that A is changing his efficiency.

Since A and B have combined efficiency of 5 units/hour, it will remain the same and we will find the time accordingly.

Does that make sense?
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Re: Work and rate problem   [#permalink] 15 Aug 2017, 23:12
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