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# Two hoses (A and B) are filling a pool. Working alone at their individ

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Math Expert
Joined: 02 Sep 2009
Posts: 58391
Two hoses (A and B) are filling a pool. Working alone at their individ  [#permalink]

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08 Oct 2018, 07:12
12
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:29) correct 33% (01:53) wrong based on 82 sessions

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Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If the two hoses work together until half the pool is full, and then Hose B finishes the pool alone, what fraction of the pool will have been filled by Hose B?

A. 1/2
B. 3/5
C. 3/4
D. 4/5
E. 7/8

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Math Expert
Joined: 02 Aug 2009
Posts: 7961
Re: Two hoses (A and B) are filling a pool. Working alone at their individ  [#permalink]

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08 Oct 2018, 08:04
Bunuel wrote:
Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If the two hoses work together until half the pool is full, and then Hose B finishes the pool alone, what fraction of the pool will have been filled by Hose B?

A. 1/2
B. 3/5
C. 3/4
D. 4/5
E. 7/8

B completes half by himself and in other half he will do more as his speed is faster than A's.
So he would do atleast $$\frac{1}{2}$$+$$\frac{1}{2}$$*$$\frac{1}{2}$$ so >1/2+1/4...>3/4..
So only D and E are left....
Now E is 7/8 so A does 1/8 work and B does 1/2-1/8=3/8.. so B does thrice the work, but the speed do not vary so much
Now D is 4/5 so A does 1/5 or 2/10 of work and B does 1/2-2/10=3/10.. so speeds 4:6 are giving similar work
D

Otherwise..
A and B together will do in..
1/4 +1/6=5/12
So work will be done in 12/5 and thus half work in 12/5*1/2=6/5

B in 6/5 days will do 6/(5*4)=3/10
Total work done is 1/2+3/10=(5+3)/10=4/5

D
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Re: Two hoses (A and B) are filling a pool. Working alone at their individ   [#permalink] 08 Oct 2018, 08:04
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