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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] New post 10 Nov 2010, 09:39
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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] New post 10 Nov 2010, 10:23
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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.

Answer: B.
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Re: A, B, C are three taps connected to a tank such that 6 times [#permalink] New post 21 Oct 2013, 12:15
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Re: Time and Work #2 [#permalink] New post 23 Oct 2013, 04:35
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.

Answer: B.


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] New post 23 Oct 2013, 05:45
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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.

Answer: B.


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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Time and Work #2 [#permalink] New post 12 Nov 2013, 21:30
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....
Can you explain this please?
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Re: Time and Work #2 [#permalink] New post 13 Nov 2013, 00:25
Expert's post
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....
Can you explain this please?


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

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Time and Work #2 [#permalink] New post 13 Nov 2013, 01:01
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....
Can you explain this please?


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] New post 13 Nov 2013, 01:10
Expert's post
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....
Can you explain this please?


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).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Time and Work #2   [#permalink] 13 Nov 2013, 01:10
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