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

Question

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

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

Giampa · Answer

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
thus answer a

generis · Answer

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

Answer A

testcracker · Answer

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 ..?

generis · Answer

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.

Mo2men · Answer

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 = 2/3 day......................(rate of A only = 3)

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

Answer: A

testcracker · Answer

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 ...

ScottTargetTestPrep · Answer

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.

Answer: A

Paul4gmat · Answer

all looks fine but one typo i guess .. phase 3 shou'd be 2/3 but its written 1/3. while calculating the total time its correctly mentioned as 2/3

Mo2men · Answer

Thanks a lot. I will edit my post

bumpbot · Answer

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

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