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# Pumps A, B and C operate at their respective rates. Pumps A

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Joined: 05 Feb 2006
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Pumps A, B and C operate at their respective rates. Pumps A [#permalink]  28 Oct 2006, 02:29
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Pumps A, B and C operate at their respective rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B and C, operating simultaneously, to fill the tank?

A) 1/3
B) 1/2
C) 2/3
D) 5/6
E) 1
SVP
Joined: 01 May 2006
Posts: 1798
Followers: 8

Kudos [?]: 102 [0], given: 0

(E) for me

Let define:

A = 1 / (Time pump A fills alone)
B = 1 / (Time pump B fills alone)
C = 1 / (Time pump C fills alone)
T : the time necesseray when all pumps apporate together

We have so:

o A + B = 5/6 (1)
o A + C = 2/3 (2)
o B + C = 1/2 (3)

and

1/T = A + B + C

(1) - (2)
<=> B-C = 5/6 - 2/3 = 1/6 (4)

(4) + (3)
<=> 2*B = 1/6 + 1/2 = 4/6 = 2/3
<=> B = 1/3

Then,

1/T = A + C + 1/3
<=> 1/T = 2/3 + 1/3
<=> 1/T = 1
<=> T = 1
Manager
Joined: 04 May 2006
Posts: 173
Location: paris
Followers: 1

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E 2

The sum of 1/a +1/b + 1/c= 1/T
It can be demonstraded that the sum of (a &b), (b&c) and (a&c) each working simultaneously is 1/k, where T=2*k
so
5/6+2/3 + 1/2=2, then K=1/2 so T=1
_________________

time is not on my side

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