Water flows into an empty tank of 54 liters via 12 small pipes. The ra

Question

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 per pipe. 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

M05-09

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

M05-09

BelalHossain046 · Accepted Answer

Total fill up 12 small pipes by 12 hours @1 liter per hour=12*12*1=144 liters
Total amount remained there after 12 hours =54 liters
So, 144-54=90 liters are OUT by some LARGE pipes which are running at 1.50 liters per hour for 12 hours I.e. 18 liters per pipe in that period 
So, number of large pipes is 90/18=5.

Bunuel · Answer

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 per pipe. 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

M05-09

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

rajatchopra1994 · Answer

Explanation:

54 liters filled in 12 hours = net fill rate = 4.5 liters per hour.

Small pipes (incoming) 12 pipes at 1 liter each = 12 liters incoming.

Net = incoming (12) minus outgoing (x) = 4.5

Therefore, the outgoing rate = 7.5

At 1.5 per hour per large pipe, 7.5/1.5 = 5 large pipes.

IMO-D

AntrikshR · Answer

12 pipes filling with the rate of 1 l/hr means tank will have 12 l in an hour.
=>In 12 hr tank would have 144 l.But there are outflow pipes and they are emptying at the rate of 1.5l/hr . It means 30 l in 12 hours.
=> 144-30x=54
=> X= 3
IMO B

Posted from my mobile device

AntrikshR · Answer

12 pipes are filling the tank with the rate of 1 l/hr means tank will have 12 l in an hour.
=>In 12 hrs tank would have 144 l.But there are outflow pipes and they are emptying the tank at the rate of 1.5l/hr . It means water is getting out at the rate of 18 l/12 hours.
=> 144-18x=54
=> X= 5
IMO D
*Did calculation mistake earlier!

frombelarus · Answer

(1 liter of inflow per small pipe * 12 hours to fill the tank * 12 small pipes) - (1,5 liter of outflow per hour per pipe * 12 hours to fill the tank * X number of large pipes) = 54 liters

1*12*12 - 1,5*12x = 54
144 - 18x = 54
18x = 90
x= 5

pierjoejoe · Answer

I did not read carefully the question and thought that both the 2 sets of tubes (bigger and smaller ones) flowed in the tank. At a certain point in the calculation, i had a negative number for the number of tubes, and thought that something was off, because it meant that some tubes were subtracting water ahah. Than, i carefully read the instruction and found out that the bigger tubes were indeed subtracting water lol

demawtf · Answer

W=r*t

official total rate 54/12=4,5

rate in = 12 pipes * 1L/1hr = 12 L / hr
rate out = x large pipes * 1,5L/1hr = 1,5x L / hr

1,5x + 12 = 4,5
x=5

ravi1522 · Answer

Hello ,
Total fill up 12 small pipes by 12 hours @1 liter per hour=12*12*1=144 liters
Total amount remained there after 12 hours =54 litres
Remaining will be 144-54=90 litres
So outlet pipe work done for 12 hrs will be =1.5*12=18 litres/hour
So no of pipes will be =90/18=5

Hence option is D

essetempore · Answer

algebraic expression
12 (1) - 1.5 (x) = 4.5
1.5x = 7.5, x=5

Water flows into an empty tank of 54 liters via 12 small pipes. The ra

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Water flows into an empty tank of 54 liters via 12 small pipes. The ra

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