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A pool can be filled in 4 hours and drained in 5 hours. The

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Re: A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 21 Jan 2015, 08:43
A simpler approach :

If we let the inlet on for 10 hours without keeping the outlet open ---> it will fill the pool 2.5 times its capacity.
Hence there is an amount of 1.5 or 6/4 in excess to be drained with a rate of 5 hours.
Therefore, it will take 1.5*5 or 7.5 hours to empty the extra amount of water.
Hence 1:00PM + 2.5 hours = 3:30PM.

Let me know if this approach is correct and faster to solve these types of questions.:)
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New post 22 Aug 2015, 14:04
Also solvable if you plug in numbers - assumed the pool has 200L capacity.

Fills in 50L / hour
Empties in 40L / hour

Relative rate is 10L/ hour.

If the drain is open at 3:30, it's already been filling up at 50L/hour for 2.5 hours = 125L full

It will continue to fill up for 7.5 hours at 10L/hour = 75L

Total = 200L you originally assumed.

Answer is D

Hope it helps!

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Re: A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 22 Aug 2015, 20:05
pool can be filled in 4 hours and drained 5 hours.
take lcm of two pipes that is 20 units.
takes 20 hours to fill pool if both the pipes opened simultaneously.

filling pipe can fill 5units/hour.

draing pipe take out 4units?hour.
pool was opened at 1 pm.
pool was filled at 11 pm. It takes 10 hours to complete it.

If drain pipe opened at 2 pm. filling pipe worked for 1 hour. so 5units work over.
remaining 15 units take additional 15 hours to fill.
if drain pipe opened at 2.30pm. filling pipe worked for 1 and 1/2 hour 7.5 units work over.
take 12. 5 units , take additional 12.5 hours to fill.
if drain pipe opened at 3 pm, 10 units units, over, 10 hours to fill.
if drain pipe opened at 3.30pm. 12.5 units over, another 7.5 units , hours take to fill.
3.30+7.30= 11pm
so option D is correct
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Re: A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 26 Aug 2015, 09:09
10/4 - x/5 = 1 not 1/10
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New post 25 Nov 2015, 04:52
1
Economist wrote:
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm

I did:
10/4 - x/5 = 1/10 ( x = number of hours drain pipe is opened ). But I cant find the answer.


m20 q32


I would rather use here smart numbers....
Pool Capacity = 100 Liters
Filling Rate (F) = \(\frac{100}{4}=25\)
Draining Rate (D) = \(\frac{100}{5}=20\)
Time =10 Hours (Start 1:00 pm End 11:00 pm)

250 Liters were filled in 10 hours --> 10*Rate(F) so we have +150 Liters that must be drained (because the filled pool must have only 100 Liters)
\(Rate (D) * t = 150\) --> \(20*t=150\), \(t=7.5 Hours\)
Answer D (11 pm - 7.5 =3:30)

Hope this approach helps....
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Re: A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 26 Mar 2018, 10:42
Bunuel

If the value was open for x hours, then why is it (11-1-x) hours when both the valve and the drain were open and not just (11−x)hours?

Thanks!
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New post 26 Mar 2018, 11:11
Economist wrote:
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm


let d=hours drain open
10*1/4-d*1/5=1
d=7.5 hours
11:00 pm-7.5 hours=3:30 pm
D
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Re: A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 31 Jul 2019, 20:38
Economist wrote:
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm

I did:
10/4 - x/5 = 1/10 ( x = number of hours drain pipe is opened ). But I cant find the answer.


m20 q32


Quick Method


Let the whole pool unit be 5 X 4 = 20
Filling per hour is 5
Draining per hour is 4

Pool was for sure filling from 1 PM to 11 PM which are 10 hours

So, filling pipe started for 10 hours
Work done by Filling Pipe = 50

Equation would be : 50 [Filling pipe ran for 10 hours 5 x 10 ] - 4x [ Draining pipe ran for some hours ] = 20 [ both need to reach this much unit of pool ]
Solving equation x = 7.5 [ Means Draining pipe ran for 7.5 hours out of 10 hours of filling operation ]

Therefore , it should have started after 2.5 hours

Hens Ans is 3:30 PM
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Re: A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 03 Aug 2019, 04:15
Let the capacity be 100 litres

Filling rate-20/hr
draining rate: -25 /hr

Filling pipe worked for 10 hours
Thus, 25*10=250
But, capacity is 100

150 must be drained by draining pipe
Thus, it will take 150/20=7.5 hours to drain

Thus, it has started 2.5 hours after 1 pm

Thus, answer=3:30PM
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A pool can be filled in 4 hours and drained in 5 hours. The  [#permalink]

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New post 03 Aug 2019, 17:25
Economist wrote:
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm


in 10 hours with drain closed, valve can fill 10/4, or 2.5 pools
so in 10 hours with valve open, drain must empty 2.5-1=1.5 pools
1.5 pools*5 hours=7.5 hours drain needs to leave pool filled at 11:00pm
11:00pm-7.5 hours=3:30pm
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A pool can be filled in 4 hours and drained in 5 hours. The   [#permalink] 03 Aug 2019, 17:25

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