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M05-09

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New post 16 Sep 2014, 00:24
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Difficulty:

  35% (medium)

Question Stats:

70% (01:45) correct 30% (01:25) wrong based on 149 sessions

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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

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New post 16 Sep 2014, 00:24
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Official Solution:

Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6


The tank is full in 12 hours, therefore, the effective inflow has to be \(\frac{54}{12} = 4.5\) liters per hour. Currently our nominal inflow is 12 liters per hour and outflow is unknown. To find the outflow, we need to subtract effective inflow from the nominal inflow. \(12 - 4.5 = 7.5\); We know that each of the large, outgoing pipes has a flow rate of 1.5 liters per hour, therefore, \(\frac{7.5}{1.5} = 5\).


Answer: D
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M05-09  [#permalink]

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New post 15 May 2015, 02:04
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Other solutions:
Let x be large pipes:
=> (1*12 - 1.5*x)*12 = 54
Solving we get x=5.
Is it right!
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Re: M05-09  [#permalink]

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New post 25 Aug 2015, 22:17
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If I may elaborate above explanation,

A = RT
54 = Final R * T
54 = (Inflow Rate - Outflow Rate) * T
54 = (12-1.5x)*12
x=5
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Re: M05-09  [#permalink]

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New post 03 Feb 2017, 09:10
Empowergmat Rich, can you pls explain this simpliest way to solve this problem
What concept am I lacking to think like Bunuel.
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New post 11 Sep 2017, 19:33
I think this is a poor-quality question and I agree with explanation. Question should explicitly note that the outflow rate of 1.5 l/h is "in each large pipe" (to borrow from the language of the preceding sentence).

Otherwise, Q is excellent as always. But the answer wouldn't make sense if one didn't assume 1.5l/h was on a per pipe basis (of course, one would eventually figure it out, but I don't think question wording should be allowed to unnecessarily cost the user time).
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M05-09   [#permalink] 11 Sep 2017, 19:33
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