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

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Intern
Joined: 19 Mar 2012
Posts: 2
Location: United States
GMAT Date: 04-17-2012
Jamal can fill the vending machine in 45 minutes. When his  [#permalink]

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19 Mar 2012, 11:38
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Question Stats:

89% (00:37) correct 11% (00:53) wrong based on 20 sessions

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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

Thank you for any help whatsoever.
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: Jamal can fill the vending machine in 45 minutes. When his  [#permalink]

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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

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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Intern
Joined: 19 Mar 2012
Posts: 2
Location: United States
GMAT Date: 04-17-2012
Re: Jamal can fill the vending machine in 45 minutes. When his  [#permalink]

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19 Mar 2012, 12:33
It does help! Thank you very much.
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Joined: 09 Sep 2013
Posts: 8195
Re: Jamal can fill the vending machine in 45 minutes. When his  [#permalink]

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08 Jun 2018, 22:21
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Re: Jamal can fill the vending machine in 45 minutes. When his &nbs [#permalink] 08 Jun 2018, 22:21
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