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# Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool

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Director
Joined: 26 Oct 2016
Posts: 681
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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31 Oct 2017, 23:29
3
KUDOS
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:12) correct 35% (02:57) wrong based on 91 sessions

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Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2
[Reveal] Spoiler: OA

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Anaira Mitch

Intern
Joined: 22 Jun 2017
Posts: 17
Location: Italy
GPA: 3.64
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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01 Nov 2017, 08:01
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This post was
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anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

First: calculate the rates for each hoses.
Ra=1/2
Rb=1/3
Rc=1/6
then sum up all rates we need:
Ra+Rb+Rb=6/6
Ra+Rc=4/6
Time to fill the pool = (1/3)/(6/6)+(1/3)/(4/6)+(1/3)/(1/2) = 18/12 = 1.5
VP
Joined: 22 May 2016
Posts: 1420
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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01 Nov 2017, 09:55
DOUBLE POST, this one deleted, APOLOGIES
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At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Last edited by generis on 01 Nov 2017, 12:52, edited 1 time in total.
VP
Joined: 22 May 2016
Posts: 1420
Re: Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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01 Nov 2017, 10:03
1
KUDOS
anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

Three stages. In all three, work, $$W$$, to be done = fill $$\frac{1}{3}$$ of pool.

All work rates are in $$\frac{pools}{hr}$$

A's rate = $$\frac{1}{2}$$. B's rate = $$\frac{1}{3}$$. C's rate = $$\frac{1}{6}$$

1) Stage 1: A,B, and C work together to fill $$W=\frac{1}{3}$$ of pool. Add rates, find time.

Combined rate:
$$(\frac{1}{2}+\frac{1}{3}+\frac{1}{6})=\frac{6}{6}= 1$$

Stage 1 time, $$(Time=\frac{Work}{rate}):$$$$\frac{(\frac{1}{3})}{1}=\frac{1}{3}hr$$

2) Stage 2. B leaves. How much work? Pool is $$\frac{1}{3}$$ full. A and C work "until it is $$\frac{2}{3}$$ full."
$$W=(\frac{2}{3}-\frac{1}{3})=\frac{1}{3}$$ to fill

Add rates of A and C, find time. Combined rate:
$$(\frac{1}{2}+\frac{1}{6})=\frac{8}{12}=\frac{2}{3}$$

Stage 2 time, ($$T=\frac{W}{r})$$:
$$\frac{(\frac{1}{3})}{(\frac{2}{3})}=\frac{1}{2}hr$$

3) Stage 3. A works alone. Pool is $$\frac{2}{3}$$ full. Work is 1 pool. So $$\frac{1}{3}$$ remains =$$W$$

Time for A to finish, $$T =\frac{W}{r}$$:
$$\frac{(\frac{1}{3})}{(\frac{1}{2})}=\frac{2}{3}hr$$

Add times for the 3 stages:
$$\frac{1}{3}+\frac{1}{2}+\frac{2}{3}hrs = 1.5 hrs$$

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 269
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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01 Nov 2017, 12:33
anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

hi

you have already scored 770. Why do you think you need to get this one solved...?
you don't need to work it out anymore, do you ..?
VP
Joined: 22 May 2016
Posts: 1420
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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01 Nov 2017, 12:50
gmatcracker2017 wrote:
anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

hi

you have already scored 770. Why do you think you need to get this one solved...?

gmatcracker2017, it is probably a good idea to tag to whom you refer. Without a "callout" it looks as if you are replying to me. I have taken the GRE and LSAT. Not the GMAT.

I think you refer to anairamitch1804 - and I think you might be confused about why non-expert persons post questions.

It is not only because the person cannot solve the problem.

Often it is simply to share, or to get points.

Maybe this problem gave her trouble (like you, I doubt it, but who cares?).

Maybe she thinks it is a good question and would like to share.

I intend no disrespect; I think you were just a little in the dark about motivations for posting questions.

I think it is a good question. In fact, I should have awarded kudos. I will do so now.
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

SVP
Joined: 26 Mar 2013
Posts: 1502
Re: Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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01 Nov 2017, 14:01
anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

Another appraoch

Let the capacity of the pool = 6 units

RA = 6/2 =3 unit/day , RB= 6/3 = 2 unit/day, RC = 6/6 = 1 unit/day

The question divides the process of filling the pool to three phases and each one equal =1/3 * 6 =2 units

Phase 1: T = 2/6 = 1/3 day.............(Total rate of 3 hoses = 1+2+3=6)

Phase 2: T = 2/4 = 1/2 day.............(rate of hoses A & C = 1+3=4)

Phase 3: T = 2/6 = 1/3 day.............(rate of A only = 3)

Total time = 1/3 + 2/3 + 1/2 = 1.5

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 269
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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02 Nov 2017, 03:14
genxer123 wrote:
gmatcracker2017 wrote:
anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

hi

you have already scored 770. Why do you think you need to get this one solved...?

gmatcracker2017, it is probably a good idea to tag to whom you refer. Without a "callout" it looks as if you are replying to me. I have taken the GRE and LSAT. Not the GMAT.

I think you refer to anairamitch1804 - and I think you might be confused about why non-expert persons post questions.

It is not only because the person cannot solve the problem.

Often it is simply to share, or to get points.

Maybe this problem gave her trouble (like you, I doubt it, but who cares?).

Maybe she thinks it is a good question and would like to share.

I intend no disrespect; I think you were just a little in the dark about motivations for posting questions.

I think it is a good question. In fact, I should have awarded kudos. I will do so now.

genxer123
hi man

please don't take it so seriously yes, of course, it is a good question
I never wanted to hurt anyone involved. So whatever your reactions might be, however, on the post, please accept my apologies
I know very well: you guys are very brilliant and helpful.
Please understand that the intended purpose of the post was only to producing some fun, nothing else, man

As always, I have full respect for everybody involved here in anyway.

take care, man

by the by, I have also awarded a kudos to the question ...

Last edited by gmatcracker2018 on 07 Nov 2017, 08:34, edited 1 time in total.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2293
Location: United States (CA)
Re: Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool [#permalink]

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02 Nov 2017, 17:02
anairamitch1804 wrote:
Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

The rates of hose A, B, and C, respectively, are 1/2, 1/3, and 1/6.

We can let t = the time it takes all 3 hoses working together to fill the first 1/3 of the pool:

(1/2)t + (1/3)t + (1/6)t = 1/3

Multiplying by 6, we have:

3t + 2t + t = 2

6t = 2

t = 1/3 hour

Next, we can let s = the time it takes hoses A and C working together to fill the next 1/3 of the pool:

(1/2)s + (1/6)s = 1/3

Multiplying by 6, we have:

3s + s = 2

4s = 2

s = 1/2 hour

Finally, we can let u = the time it takes hose A to fill the last 1/3 of the pool:

(1/2)u = 1/3

u/2 = 1/3

3u = 2

u = 2/3 hour

So, the total time is 1/3 + 1/2 + 2/3 = 2/6 + 3/6 + 4/6 = 9/6 = 3/2 = 1.5 hours.

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Re: Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool   [#permalink] 02 Nov 2017, 17:02
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