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

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New post 25 Nov 2015, 04:52
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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

[Reveal] Spoiler:
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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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, 10:49
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mahrah wrote:
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!


The valve was opened from 1:00 pm to 11:00 pm, so for 11 - 1 = 10 hours. If x is the amount of time when only the valve was open, then 10 - x is the amount of time when both the valve and the drain were open.
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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 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 28 Mar 2018, 02:51

Solution



Given:
    • The pool can be filled in 4 hours
    • The pool can be drained in 5 hours.
    • Filling valve was opened at 1:00 pm
    • The Pool was filled at 11:00 pm

Working out:

We need to find out the time when the drain valve was opened.

Per our conceptual knowledge, we know that the total volume of the pool can be taken as the LCM of 4 and 5.
    Thus, let’s assume that the total volume of the pool = 20 Liters.

Since the pool can be filled in 4 hours, in 1 hour, the amount of water filled in it = 5 litres.
Similarly, the amount of water drained in 1 hour = 4 litres.

Let’s also assume that the time after which the drain valve was opened = x hours.
So, from 1 pm to (1+x) pm, the pool was being filled at the rate of 5 liters per hour.
And from (1+x) pm to 11 pm, the pool was filled at a rate of (5-4) = 1 liter per hour.

Thus,
    • 5*x+ 1(10-x) = 20
    • Or, 5x + 10 -x = 20
    • Or, 4x = 10
    • Or, x =2.5 hours.

Thus, the drain valve was opened at 1+ 2:30 hours = 3:30 pm.

Answer: Option D
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Re: A pool can be filled in 4 hours and drained in 5 hours. The   [#permalink] 28 Mar 2018, 02:51

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