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Flow Rida (m05q09)

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Flow Rida (m05q09) [#permalink] New post 12 Nov 2008, 12:23
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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?

(A) 2.5
(B) 3
(C) 4
(D) 5
(E) 6

[Reveal] Spoiler: OA
D

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Re: Flow Rida [#permalink] New post 12 Nov 2008, 12:38
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bigfernhead wrote:
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?
2.5
3
4
5
6


so in 1 hour we get 12 liters, 54 liters will take 54/12 =4.5 hours.

bu it takes 12 hours to fill up, which means 12-4.5hours=7.5hrs are due to big pipes

7.5/1.5 or 75/15 =15/3 or 5 pipes
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Re: Flow Rida [#permalink] New post 12 Nov 2008, 12:46
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Total Inflow = # of pipes x Time x Flow rate per pipe per hour
Substituting we get, Total Inflow = 12 x 12 x 1 = 144

Total Outflow follows the same calculation = # of pipes x Time x Flow rate per pipe per hour
So Total Outflow = N x 12 x 1.5

We are told that at the end of 12 hours, the tank is Full. So
Total Inflow - Total Outflow = 54
144 - N x 18 = 54, Or
N = 90/18 = 5

My pick D
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Re: Flow Rida [#permalink] New post 12 Nov 2008, 13:53
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bigfernhead wrote:
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?

2.5
3
4
5
6


54= 12*12 - 1.5*N*12 = 144-18N
N= 90/18 =5
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Re: Flow Rida (m05q09) [#permalink] New post 03 Sep 2009, 02:13
Great approach masuhari!!
I like the subject of the topic..Flo Rida -Right round anyone?! :P
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Re: Flow Rida (m05q09) [#permalink] New post 16 Feb 2010, 03:14
bigfernhead wrote:
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?

(A) 2.5
(B) 3
(C) 4
(D) 5
(E) 6

[Reveal] Spoiler: OA
D

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Total inflow in 12 hr = 1*12*12 = 144
Tank limit = 54
Total outflow in 12 hr = 1.5*12*N = 144 - 54 = 90

so N = 5
hence D
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Re: Flow Rida (m05q09) [#permalink] New post 16 Feb 2010, 11:57
N = (12x12-54)/(1,5x12)=90/18 = 5 or
N = (12-54/12)/1,5 = 7.5/1,5 = 5
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Re: Flow Rida (m05q09) [#permalink] New post 16 Feb 2010, 15:55
Its D
equation is
(12-n*1.5)12=54
=> n= 5
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Re: Flow Rida (m05q09) [#permalink] New post 16 Feb 2010, 23:59
D

Let X be number of big pipes, then
12*12 =54 + 1.5X*12
solves X = 5
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Re: Flow Rida (m05q09) [#permalink] New post 18 Feb 2010, 08:58
Answer is D.) 5

If the tank fills up to 54L in 12 hours then it is keeping 4.5L per hour. If the small pipes are putting in 12L per hour that means that 12L - 4.5L = 7.5L being lost out of the big tank per hour. Loss of an individual big pipe per hour is 1.5L so take 7.5 / 1.5 and that gives you 5 big pipes.

Hopefully somebody knows to shut off the water or it's going to make a mess.
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Re: Flow Rida (m05q09) [#permalink] New post 05 Sep 2010, 09:02
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This can be solved as a combined work rates problem:

1/Total Time = 1/A - 1/B, where

Total Time = 12 hours, A = 4.5 hours to fill tank, & B = 36 hours to empty tank per X pipes

1/12 = 1/4.5 - X/36,

3/36 = 8/36 - x/36,

-5/36 = -x/36,

X = 5
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Re: Flow Rida (m05q09) [#permalink] New post 21 Feb 2011, 15:06
I am good with math... except word problems, I always have a hard time setting up the problem. In this particular case, (for my benefit) I drew a little picture that represents the tank, and then drew a line that assumed a rate of 12 liters per hour going in. Then because I started to panic, I just selected C at random and tried it. I found that after 12 hours, it would overflow at 72 liters. So I knew that more material had to exit the tank, meaning I would try adding a pipe. I tried answer D, plugged it in and it worked. Not sure if I was just lucky or what... I ultimately got to the answer, but I wish I knew how to set up the problem automatically like many people here in the forum.
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Re: Flow Rida (m05q09) [#permalink] New post 22 Feb 2011, 14:34
Nice equation setup. I need to get better at this. I picked numbers to come up with the answer to this problem though and was lucky enough to hit D on the first try.
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Re: Flow Rida (m05q09) [#permalink] New post 23 Feb 2011, 08:52
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I did this

12pipes 1/lph= 12lhp * 12 hrs = 144.

144-54(tank size)=90

90(gallons out)/12(hourly)=7.5(gallons removed per hour)

7.5/1.5=5.
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Re: Flow Rida (m05q09) [#permalink] New post 26 Feb 2011, 03:39
rate * time = Volume
rate inflow > rate outflow
rate inflow = 12 lit/hr and rate outflow = 1.5n lit/hr where n = pipes
(12 - 1.5n)*time = 54 lit (capacity of tank). Here time=12hrs.
Substituting n=5
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Re: Flow Rida (m05q09) [#permalink] New post 08 Mar 2011, 16:00
Answer is 5. Here is how I arrived at it:

54 is the total ending volume. We know that inflows occur at a rate of 12 liters per hour (1 liter per hour for 12 small pipes). It says in the prompt that the entire tank is full after 12 hours. Therefore we can take 144 - 54 = 90 (90 is the amount that has flowed out of the tank in this 12 hour time). We then take 90/12 = 7.5 to find out 7.5 liters flows out per hour. Then 7.5/1/5 = 5. (total liters per hour divided by rate per large pipe to yield total number of large pipes).
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Re: Flow Rida (m05q09) [#permalink] New post 23 Feb 2012, 05:14
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D

inflow of water(12 hrs) = 12*12 = 144,
But total water in the tank after 12 hrs = 54
Outflow of water (12 hrs) = (144-54) = 90/12 = 7.5
Outflow capacity = 1.5.
So total number of outflow pipes = 7.5/1.5 = 5
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Re: Flow Rida (m05q09) [#permalink] New post 26 Feb 2013, 07:49
IMO - D

Rate(Total flow) = Rate(Flow-In) - Rate(Flow-out)

12 Hrs * X liters/hr = 54 liters

- 12 hrs * 4 liters/hr = 48 liters
- 12 hrs * 5 liters/hr = 60 liters

To get 54 liters in 12 hrs the Rate(Total flow) is between 4 liters/hr and 5 liters/hr

Plug in option from the answer choices - D fits
Rate(Flow-In) = 12 liters/hr (12 pipes)
Rate(Flow-out) = 7.5 liters/hr (5 pipes)

12 hrs * 4.5 liters/hr = 54 liters
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Re: Flow Rida (m05q09) [#permalink] New post 26 Feb 2013, 09:42
In 12 hours, 12 pipes will fill the tank by 12*12 = 144 litres.
But as the tank can only take 54 litres, 144 - 54 = 90 litres should be the outgoing water.

As 1.5 litre is the size of the outgoing tube, in 12 hours 90/(12*1.5) = 5 pipes will be used to drain out the excess water.
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Re: Flow Rida (m05q09) [#permalink] New post 26 Feb 2013, 21:16
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Tank Capacity = 54 L

Total In=12 Pumps 1 L/hr for 12 hrs= 12*12=144L

Total Out = 144-54=90 L

No of outlet pumps = 90/(12 *1.5) = 5

Answer = D
Re: Flow Rida (m05q09)   [#permalink] 26 Feb 2013, 21:16
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