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# There are small hoses and large hoses filling a swimming pool. Each of

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
There are small hoses and large hoses filling a swimming pool. Each of  [#permalink]

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20 Nov 2019, 01:40
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:01) correct 31% (02:13) wrong based on 42 sessions

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There are small hoses and large hoses filling a swimming pool. Each of the three small hoses works at 2/3 the rate of one large hose. If all four hoses work at the same time, in what fraction of the time should the pool be filled if the large hose worked alone?

A 1/3
B 2/3
C 3/4
D 4/5
E 4/7

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Joined: 10 Oct 2017
Posts: 27
GMAT 1: 610 Q41 V35
Re: There are small hoses and large hoses filling a swimming pool. Each of  [#permalink]

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20 Nov 2019, 01:50
Bunuel wrote:
There are small hoses and large hoses filling a swimming pool. Each of the three small hoses works at 2/3 the rate of one large hose. If all four hoses work at the same time, in what fraction of the time should the pool be filled if the large hose worked alone?

A 1/3
B 2/3
C 3/4
D 4/5
E 4/7

if large hose does 1 work in L hours . then it will do 1/L work in 1 hours.
So small hose will do [2][/3L] . 3 small plus one larger =3*2/3L+1/L=3/L.
so (1/3)/1= 1/3
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Joined: 16 Feb 2015
Posts: 176
Location: United States
Concentration: Finance, Operations
There are small hoses and large hoses filling a swimming pool. Each of  [#permalink]

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Updated on: 20 Nov 2019, 08:36
2
Bunuel wrote:
There are small hoses and large hoses filling a swimming pool. Each of the three small hoses works at 2/3 the rate of one large hose. If all four hoses work at the same time, in what fraction of the time should the pool be filled if the large hose worked alone?

A 1/3
B 2/3
C 3/4
D 4/5
E 4/7

let large hose rate is X

3 small hose works at a 2/3X rate of large.

So, therefore, all 3 small hose flow rate= 3*(2/3)*X = 2X

If only one large hose is working/when all hoses are working= X/3X = 1/3

Please provide kudos, if you find my explanation good enough

Originally posted by rajatchopra1994 on 20 Nov 2019, 02:11.
Last edited by rajatchopra1994 on 20 Nov 2019, 08:36, edited 1 time in total.
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Joined: 27 Apr 2015
Posts: 24
Location: Singapore
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.32
There are small hoses and large hoses filling a swimming pool. Each of  [#permalink]

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20 Nov 2019, 08:19
1
rajatchopra1994 wrote:
Bunuel wrote:
There are small hoses and large hoses filling a swimming pool. Each of the three small hoses works at 2/3 the rate of one large hose. If all four hoses work at the same time, in what fraction of the time should the pool be filled if the large hose worked alone?

A 1/3
B 2/3
C 3/4
D 4/5
E 4/7

Let the Swimming pool is of 5 liters.

3 small hose works at a 2/3 rate of large.

let large hose rate is 3 litre/min.
So, therefore, all 3 small hose flow rate= 2litres/min (individually 0.666 litres /minutes)

when all hoses are working then, it will fill in 1min

If only one large hose is working = 5/3= 1.66 mins

the fraction of the time should the pool be filled=1.66-1/1= 0.66= 2/3.

Hi RajatChopra1994,
Each of the three small hoses works at 2/3 rate of the big hose, so the calculation for all three small hoses working together will equal 2*big hose. Please verify.

Solution: Let the three small hoses be a,b,c, and the big hose be A.
Now, the 3 small hoses with 2/3 rate of A, when working together (a+b+c) will accomplish (2/3 +2/3+2/3)A = 2*A work
When the 3 small hoses and the big hose work together then the work done is 2A + A = 3A

The question asks What is the fraction of time taken for Large hose working alone(A) to all 4 hoses working together (3A)
A/3A = 1/3
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Joined: 16 Feb 2015
Posts: 176
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Re: There are small hoses and large hoses filling a swimming pool. Each of  [#permalink]

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20 Nov 2019, 08:28
navaneethmmb wrote:
rajatchopra1994 wrote:
Bunuel wrote:
There are small hoses and large hoses filling a swimming pool. Each of the three small hoses works at 2/3 the rate of one large hose. If all four hoses work at the same time, in what fraction of the time should the pool be filled if the large hose worked alone?

A 1/3
B 2/3
C 3/4
D 4/5
E 4/7

Let the Swimming pool is of 5 liters.

3 small hose works at a 2/3 rate of large.

let large hose rate is 3 litre/min.
So, therefore, all 3 small hose flow rate= 2litres/min (individually 0.666 litres /minutes)

when all hoses are working then, it will fill in 1min

If only one large hose is working = 5/3= 1.66 mins

the fraction of the time should the pool be filled=1.66-1/1= 0.66= 2/3.

Hi RajatChopra1994,
Each of the three small hoses works at 2/3 rate of the big hose, so the calculation for all three small hoses working together will equal 2*big hose. Please verify.

Solution: Let the three small hoses be a,b,c, and the big hose be A.
Now, the 3 small hoses with 2/3 rate of A, when working together (a+b+c) will accomplish (2/3 +2/3+2/3)A = 2*A work
When the 3 small hoses and the big hose work together then the work done is 2A + A = 3A

The question asks What is the fraction of time taken for Large hose working alone(A) to all 4 hoses working together (3A)
A/3A = 1/3

Yes, i misunderstoood the question. Will update my answer

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Re: There are small hoses and large hoses filling a swimming pool. Each of   [#permalink] 20 Nov 2019, 08:28
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