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Bunuel
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Three filling pipes R, S and T together can fill an empty tank in 2 ho 31 Jan 2022, 05:45
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45% (02:48) correct 55% (03:11) wrong based on 60 sessions

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Three filling pipes R, S and T together can fill an empty tank in 2 hours, S can fill the tank four times faster than T. Initially R alone is opened and after 'x' hours, it is closed and immediately S and T are opened together. The tank is full after another 'y' hours. If the tank was filled in a total of 4 hours, and x is not equal to y, what is the time (in hours) that T alone would take to fill the tank?

(A) 6
(B) 12
(C) 20
(D) 24
(E) 28


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C
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KarishmaB
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Three filling pipes R, S and T together can fill an empty tank in 2 ho Updated on: 07 Apr 2025, 00:07
Originally posted by KarishmaB on 28 Mar 2022, 23:34.
Last edited by KarishmaB on 07 Apr 2025, 00:07, edited 1 time in total.
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Bunuel
Three filling pipes R, S and T together can fill an empty tank in 2 hours, S can fill the tank four times faster than T. Initially R alone is opened and after 'x' hours, it is closed and immediately S and T are opened together. The tank is full after another 'y' hours. If the tank was filled in a total of 4 hours, and x is not equal to y, what is the time (in hours) that T alone would take to fill the tank?

(A) 6
(B) 12
(C) 20
(D) 24
(E) 28


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First of all, this is a problem solving question so it is bound to have a unique solution.
All three together take 2 hrs so their combines rate is 1/2 tank per hour.
But R is opened alone separately and S and T are opened together but independently of R. The time taken in this case is 4 hrs, twice of time taken before. This happens when the rate of work of 2 individuals/groups is equal. When they work together, time taken is half of time taken when they work independently.
So rate of R must be equal to rate of S and T together.
If rate of T is T, rate of S is 4T (four times rate of T). Then rate of R is 5T (same as combined rate of S and T).

Combined rate of all three = T + 4T + 5T = 10T = 1/2 tank per hour
Rate of T = 1/20th tank per hour

Time taken by T alone is 20 hrs.

Answer (C)

Note that it doesn't matter what x and y are. They could be 1 and 3 respectively or 1.5 and 2.5 or 2.1 and 1.9 etc. Since both the rates are same ('Rate of R alone' = 'Rate of S+T') time taken will be 4 hrs only. Whether we make only R work or S and T work, it has the same effect.

For more on this, check out the work-rate module here using the 3 day trial: https://anaprep.com
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Three filling pipes R, S and T together can fill an empty tank in 2 ho 31 Jan 2022, 17:14
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Bunuel
Three filling pipes R, S and T together can fill an empty tank in 2 hours, S can fill the tank four times faster than T. Initially R alone is opened and after 'x' hours, it is closed and immediately S and T are opened together. The tank is full after another 'y' hours. If the tank was filled in a total of 4 hours, and x is not equal to y, what is the time (in hours) that T alone would take to fill the tank?

(A) 6
(B) 12
(C) 20
(D) 24
(E) 28

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Breaking Down the Info:

Let R, S, and T be the rates of the pipes.

R, S and T together can fill an empty tank in 2 hours: \(R + S + T = \frac{1}{2}\)

S can fill the tank four times faster than T: \(S = 5T\), therefore \(S + T = 6T\)

For the next part on x and y, we have \(R*x + (S + T)*y = 1\). Our goal is to find T, so plug out everything else and leave only T and x.

Plug in \(y = 4 - x\) and \(R = \frac{1}{2} - 6T\) to get \((0.5 - 6T)*x + (6T)(4 - x) = 1\)

Simplifying gives \(-12Tx + 24T = 1 - 0.5x\) and \(T = \frac{1 - 0.5x }{ 24 - 12x} = \frac{1}{24}\)

Thus it would take T 24 hours alone.

Answer: D
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Three filling pipes R, S and T together can fill an empty tank in 2 ho 28 Mar 2022, 06:48
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Bunuel KarishmaB
Can you post the correct solution for this ?
I solved this question using this approach, please help me if I made any unreasonable assumption
Let R, S, and T be the rates of the pipes.
R, S and T together can fill an empty tank in 2 hours: R+S+T=1/2
Also S = 4T
R + 5T = = 1/2 ..........................................................................I
We are given x(R) + 5(yT) = 1
Now, x+y=4 & x!=y and also S completes stuff 4 times faster than T, So breaking x+y=4 into 1 and 3 , i.e. x=1 , y=3
Even if we flip the number and solve for T we get the same result.
R + 15T = 1................................................................................II
Substracting I from II
T = 1/20
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Three filling pipes R, S and T together can fill an empty tank in 2 ho 28 Mar 2022, 11:01
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JerryAtDreamScore
Bunuel


\(T = \frac{1 - 0.5x }{ 24 - 12x} = \frac{1}{24}\)

Thus it would take T 24 hours alone.

Answer: D
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How did you solve the fraction? I didn't get that part.

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Three filling pipes R, S and T together can fill an empty tank in 2 ho 03 Oct 2024, 03:03
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