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Jamal can fill the vending machine in 45 minutes. When his

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Jamal can fill the vending machine in 45 minutes. When his [#permalink] New post 19 Mar 2012, 11:38
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Hi,

I have this problem I'm trying to figure out:

Jamal can fill the vending machine in 45 minutes. When his sister, Violet, helps him, it takes them 20 minutes. How long would it take Violet to fill the machine by herself?

The solution formula the textbook provides is:

20/x + 20/45 = 1

This is confusing to me, because shouldn't the logic of it work like this:

Work by Jamal/Total Work by both + Work by Violet (x)/ Work by both = 1

, or 45/20 + x/20 = 1?

P.S. I know that often they recommend to break down work rate to a unit of time. So, in Jamal's case it would be 1/45, and total rate would be 1/20. So, in that case 1/45:1/20, actually, would mean 20/45. But is 1/45:1/20 + x:1/20 = 1? Isn't 1 a 100%, and in this case 1 is what?? I'm confused :shock:

Thank you for any help whatsoever.
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Re: Jamal can fill the vending machine in 45 minutes. When his [#permalink] New post 19 Mar 2012, 12:13
EugeneZelenyi wrote:
Hi,

I have this problem I'm trying to figure out:

Jamal can fill the vending machine in 45 minutes. When his sister, Violet, helps him, it takes them 20 minutes. How long would it take Violet to fill the machine by herself?

The solution formula the textbook provides is:

20/x + 20/45 = 1

This is confusing to me, because shouldn't the logic of it work like this:

Work by Jamal/Total Work by both + Work by Violet (x)/ Work by both = 1

, or 45/20 + x/20 = 1?

P.S. I know that often they recommend to break down work rate to a unit of time. So, in Jamal's case it would be 1/45, and total rate would be 1/20. So, in that case 1/45:1/20, actually, would mean 20/45. But is 1/45:1/20 + x:1/20 = 1? Isn't 1 a 100%, and in this case 1 is what?? I'm confused :shock:

Thank you for any help whatsoever.


Welcome to GMAT Club. Below is a solution for your question.

Jamal can fill the vending machine in 45 minutes. When his sister, Violet, helps him, it takes them 20 minutes. How long would it take Violet to fill the machine by herself?

Say Violet needs x minute to fill the machine by herself, so her rate is 1/x job/minute. Since Jamal can fill the vending machine in 45 minutes then his rate is 1/45 job/minute. Their combined rate would be 1/x+1/45, which as we are told equal to 1/20 job/minute, so 1/x+1/45=1/20 --> x=36 minute.

Generally for multiple entities: \frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}, where T is time needed for these entities to complete a given job working simultaneously.

Check this for more on this subject: two-consultants-can-type-up-a-report-126155.html#p1030079

Hope it helps.
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Joined: 19 Mar 2012
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Re: Jamal can fill the vending machine in 45 minutes. When his [#permalink] New post 19 Mar 2012, 12:33
It does help! Thank you very much.
Re: Jamal can fill the vending machine in 45 minutes. When his   [#permalink] 19 Mar 2012, 12:33
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