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# A, B, C are three taps connected to a tank such that 6 times

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A, B, C are three taps connected to a tank such that 6 times [#permalink]

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10 Nov 2010, 10:39
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A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?

A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
[Reveal] Spoiler: OA

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Re: Time and Work #2 [#permalink]

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10 Nov 2010, 11:23
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cleetus wrote:
A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?

A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs

Check this: word-translations-rates-work-104208.html?hilit=time%20work#p812628

Let a, b and c be the time needed for A, B and C respectively to fill the tank alone.

Given:
$$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$ - combined rate of B and C is 7/6 of rate of A;

$$\frac{10}{3}*\frac{1}{c}=\frac{1}{a}+\frac{1}{b}$$ - combined rate of A and B is 10/3 of rate of C;

$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{60}$$ - combined rate of A, B and C is 13/60 tank/hour;

Solving:
$$\frac{1}{a}+\frac{7}{6a}=\frac{13}{60}$$ --> $$a=10$$;

$$\frac{1}{c}+\frac{10}{3c}=\frac{13}{60}$$ --> $$c=20$$;

$$\frac{1}{10}+\frac{1}{b}+\frac{1}{20}=\frac{13}{60}$$ --> $$b=15$$.

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Re: A, B, C are three taps connected to a tank such that 6 times [#permalink]

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21 Oct 2013, 13:15
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Re: Time and Work #2 [#permalink]

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23 Oct 2013, 05:35
Bunuel wrote:
cleetus wrote:
A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?

A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs

Check this: word-translations-rates-work-104208.html?hilit=time%20work#p812628

Let a, b and c be the time needed for A, B and C respectively to fill the tank alone.

Given:
$$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$ - combined rate of B and C is 7/6 of rate of A;

$$\frac{10}{3}*\frac{1}{c}=\frac{1}{a}+\frac{1}{b}$$ - combined rate of A and B is 10/3 of rate of C;

$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{60}$$ - combined rate of A, B and C is 13/60 tank/hour;

Solving:
$$\frac{1}{a}+\frac{7}{6a}=\frac{13}{60}$$ --> $$a=10$$;

$$\frac{1}{c}+\frac{10}{3c}=\frac{13}{60}$$ --> $$c=20$$;

$$\frac{1}{10}+\frac{1}{b}+\frac{1}{20}=\frac{13}{60}$$ --> $$b=15$$.

Hi Bunuel,

I have a really stupid question, but I hope you can help me out. Why isn't it 6 (1/A) = 7(1/B + 1/C) leading to a final equation of 6/7 (1/A) = 1/B + 1/C?

Thanks in advanced - as always!!

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Re: Time and Work #2 [#permalink]

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23 Oct 2013, 06:45
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pauc wrote:
Bunuel wrote:
cleetus wrote:
A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?

A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs

Check this: word-translations-rates-work-104208.html?hilit=time%20work#p812628

Let a, b and c be the time needed for A, B and C respectively to fill the tank alone.

Given:
$$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$ - combined rate of B and C is 7/6 of rate of A;

$$\frac{10}{3}*\frac{1}{c}=\frac{1}{a}+\frac{1}{b}$$ - combined rate of A and B is 10/3 of rate of C;

$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{60}$$ - combined rate of A, B and C is 13/60 tank/hour;

Solving:
$$\frac{1}{a}+\frac{7}{6a}=\frac{13}{60}$$ --> $$a=10$$;

$$\frac{1}{c}+\frac{10}{3c}=\frac{13}{60}$$ --> $$c=20$$;

$$\frac{1}{10}+\frac{1}{b}+\frac{1}{20}=\frac{13}{60}$$ --> $$b=15$$.

Hi Bunuel,

I have a really stupid question, but I hope you can help me out. Why isn't it 6 (1/A) = 7(1/B + 1/C) leading to a final equation of 6/7 (1/A) = 1/B + 1/C?

Thanks in advanced - as always!!

6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank:

Time taken by A is a.
Time taken by B and C together to fill the tank is reciprocal of combined rate of B and C, thus it's bc/(b+c).

Given: $$6a=7*\frac{bc}{b+c}$$ --> $$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$.

Hope it's clear.
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Re: Time and Work #2 [#permalink]

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12 Nov 2013, 22:30
Bunuel wrote:
6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank:

Time taken by A is a.
Time taken by B and C together to fill the tank is reciprocal of combined rate of B and C, thus it's bc/(b+c).

Given: $$6a=7*\frac{bc}{b+c}$$ --> $$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$.

Hope it's clear.

Isn't time taken by A supposed to be (1/a)?
And 6 time the time taken by A in 6*(1/a) as per the R*T=W?
I don't get how it's possible to say that a is the time taken by A, and then
when multiplying, you do the multiplication and only then take the reciprocal....

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Re: Time and Work #2 [#permalink]

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13 Nov 2013, 01:25
ronr34 wrote:
Bunuel wrote:
6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank:

Time taken by A is a.
Time taken by B and C together to fill the tank is reciprocal of combined rate of B and C, thus it's bc/(b+c).

Given: $$6a=7*\frac{bc}{b+c}$$ --> $$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$.

Hope it's clear.

Isn't time taken by A supposed to be (1/a)?
And 6 time the time taken by A in 6*(1/a) as per the R*T=W?
I don't get how it's possible to say that a is the time taken by A, and then
when multiplying, you do the multiplication and only then take the reciprocal....

a is the time taken by A, because I denoted it that way.
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Re: Time and Work #2 [#permalink]

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13 Nov 2013, 02:01
Bunuel wrote:
ronr34 wrote:
Bunuel wrote:
6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank:

Time taken by A is a.
Time taken by B and C together to fill the tank is reciprocal of combined rate of B and C, thus it's bc/(b+c).

Given: $$6a=7*\frac{bc}{b+c}$$ --> $$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$.

Hope it's clear.

Isn't time taken by A supposed to be (1/a)?
And 6 time the time taken by A in 6*(1/a) as per the R*T=W?
I don't get how it's possible to say that a is the time taken by A, and then
when multiplying, you do the multiplication and only then take the reciprocal....

a is the time taken by A, because I denoted it that way.

If so, then why did you take the reciprocal of it for the equations?
Why not leave them with a,b, and c?
I am missing something, but I can't tell what....

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Re: Time and Work #2 [#permalink]

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13 Nov 2013, 02:10
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ronr34 wrote:
Bunuel wrote:
ronr34 wrote:
Isn't time taken by A supposed to be (1/a)?
And 6 time the time taken by A in 6*(1/a) as per the R*T=W?
I don't get how it's possible to say that a is the time taken by A, and then
when multiplying, you do the multiplication and only then take the reciprocal....

a is the time taken by A, because I denoted it that way.

If so, then why did you take the reciprocal of it for the equations?
Why not leave them with a,b, and c?
I am missing something, but I can't tell what....

I think you should go through the basics once more. For example, check here: work-word-problems-made-easy-87357.html or here: two-consultants-can-type-up-a-report-in-12-5-hours-and-edit-126155.html#p1030079

(time)*(rate)=)(job done), thus time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job --> 1/6 of the job will be done in 1 hour (rate).
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Re: A, B, C are three taps connected to a tank such that 6 times [#permalink]

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13 Dec 2015, 12:42
Hello from the GMAT Club BumpBot!

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Re: A, B, C are three taps connected to a tank such that 6 times [#permalink]

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23 Dec 2016, 23:47
Hello from the GMAT Club BumpBot!

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Re: A, B, C are three taps connected to a tank such that 6 times [#permalink]

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24 Dec 2016, 04:41
Bunuel wrote:
cleetus wrote:
A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?

A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs

Check this: word-translations-rates-work-104208.html?hilit=time%20work#p812628

Let a, b and c be the time needed for A, B and C respectively to fill the tank alone.

Given:
$$\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}$$ - combined rate of B and C is 7/6 of rate of A;

$$\frac{10}{3}*\frac{1}{c}=\frac{1}{a}+\frac{1}{b}$$ - combined rate of A and B is 10/3 of rate of C;

$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{60}$$ - combined rate of A, B and C is 13/60 tank/hour;

Solving:
$$\frac{1}{a}+\frac{7}{6a}=\frac{13}{60}$$ --> $$a=10$$;

$$\frac{1}{c}+\frac{10}{3c}=\frac{13}{60}$$ --> $$c=20$$;

$$\frac{1}{10}+\frac{1}{b}+\frac{1}{20}=\frac{13}{60}$$ --> $$b=15$$.

Hi Bunuel, how good one should be to finish this problem in 2 min? Because I spent 1:30 to set up all the equations, and even if the solving part is not that complicated it is not even that quick.

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Re: A, B, C are three taps connected to a tank such that 6 times   [#permalink] 24 Dec 2016, 04:41
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