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A water reservoir has two inlets and one outlet. Through the inlets wa

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A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post Updated on: 09 Oct 2018, 19:56
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A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm

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Originally posted by Tashin Azad on 09 Oct 2018, 17:44.
Last edited by Bunuel on 09 Oct 2018, 19:56, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 09 Oct 2018, 22:12
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Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm


What happens till 3 o clock?

Inlet A has been open for 2 hrs so has done 2/3 of the work (filling one reservoir)
Inlet B has been open for 1 hr so has done 1/3.75 = 100/375 = 4/15 of the work
Together, 2/3 + 4/15 = 14/15 of the reservoir is full.

From 3 o clock onwards the total rate of work done on the reservoir = 1/3 + 4/15 - 1 = -6/15
So to empty out 14/15 of the reservoir, time taken will be (14/15)/(6/15) = 7/3 hrs = 2 hrs and (1/3) hr = 2 hrs and 20 mins

By 5:20, the reservoir will be empty.

Answer (C)
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A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 09 Oct 2018, 21:33
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From 1:00 pm - 2:00 pm
1 inlet will fill 33% of the water reservoir
It takes 3 hours to fill the whole reservoir, so in 1 hour it will fill = 100/3 = 33%
From 2:00 pm - 3:00 pm
2nd inlet will fill 27% (approx)
It takes 3 hours and 45 minutes (225 minutes) to fill the whole reservoir, so in 1 hour it will fill = 1/225 *60 = 27% (approx).
Combined rate(33%+27%) = 60%.
Therefore, 60% + 33% = 93%
From 3:00 pm - 4:00 pm
It takes 1 hour for the outlet to empty the reservoir.
Therefore, 93% + 60% = 153%
153 - 100% = 53% water left in water reservoir
From 4:00 pm - 5:00 pm
53% + 60% = 113%
113% - 100% = 13% water left in water reservoir
We can see in every minute there is 1% increase in water, but for every minute there is 100/60 = 1.67% decrease in water
Therefore, in next 20 minutes water level will be 33% (13% +20%), and the deduction rate will also be 33% (100/60 * 20)
33% - 33% = 0

Ans : 5:20 pm (C)


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Hope it helps
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Re: A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 10 Oct 2018, 00:00
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm

Inlet 1: time 3 hrs: and inlet 2 : time 3 hrs 45 mins: 15/4 hrs
Outlet time given : 1 hr

Rate for inlet 1 : 1/3 , inlet 2 4/15, inlet 3 : 1

since the outlet valve gets opened at 3pm and in relative to it inlet valve opens at 1 pm and 2 pm so we can say:

=> (x-2)/3+ (x-1)*15/4-x=1
Solve for x we would get x= 65/37 ~ 1.75 hrs
We can say that time it would take to empty tank would be 3+1.75 hrs viz. ~ 5:25 mins or option C...
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A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 11 Oct 2018, 08:05
Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm


let inlets be A and B

A rate is \(\frac{1}{180}\)(i.e 3 hours is 180 minutes)

B rate is \(\frac{1}{225}\) i.e. (3 hrs and 45 min is 225 minutes)

Combined rate:\(\frac{1}{180} + \frac{1}{225} = \frac{9}{900}i.e. \frac{1}{100}\)
So total work units is 100 complete a job, BUT since A worked alone for one hour i.e 60 min, we need to subtract 100-60 =40 so 40 work units are left

let X be total time required when B is activated while A keeps working hence x-40

\(\frac{1}{180} + \frac{1}{100} *x-40 = 1\)

\(5+9(x-40) = 900\)

\(5+9x-360 =900\)

\(9x= 1255\)

\(x = 139.4\) (round to 140)

So, 140 minutes is 2 hours and 20 minutes

if work started at 1 pm then it will be complted at 3.20 , ans by 4.20 emptied :?


Bunuel, pushpitkc, chetan2u VeritasKarishma, generis whats wrong with my solution :-)

p.s. I followed the method of similar problem here https://gmatclub.com/forum/two-taps-can ... l#p2142371
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A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 11 Oct 2018, 16:01
1
dave13 wrote:
Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm

let inlets be A and B

A rate is \(\frac{1}{180}\)(i.e 3 hours is 180 minutes)

B rate is \(\frac{1}{225}\) i.e. (3 hrs and 45 min is 225 minutes)

Combined rate:\(\frac{1}{180} + \frac{1}{225} = \frac{9}{900}i.e. \frac{1}{100}\)
So total work units is 100 complete a job, BUT since A worked alone for one hour i.e 60 min, we need to subtract 100-60 =40 so 40 work units are left

let X be total time required when B is activated while A keeps working hence x-40

\(\frac{1}{180} + \frac{1}{100} *x-40 = 1\)

\(5+9(x-40) = 900\)

\(5+9x-360 =900\)

\(9x= 1255\)

\(x = 139.4\) (round to 140)

So, 140 minutes is 2 hours and 20 minutes

if work started at 1 pm then it will be complted at 3.20 , ans by 4.20 emptied :?

Bunuel, pushpitkc, chetan2u VeritasKarishma, generis whats wrong with my solution :-)

p.s. I followed the method of similar problem here https://gmatclub.com/forum/two-taps-can ... l#p2142371

Hi dave13 , that method doesn't really apply; we don't need to find your \(x\) for the first part. Time is given. In the second part, all three pipes work. A and B don't stop.
Generally, when minutes' totals are large, I switch to hours. Finally, I think this math is easier broken into stages.

(1) How much of reservoir is filled in 2 hours by A and B?

Pipe A rate: \(\frac{1R}{3hrs}=\frac{1}{3}\)

Pipe B rate* = \(\frac{4}{15}\)

Combined rate of A and B: \((\frac{1}{3}+\frac{4}{15})=\frac{9}{15}=\frac{3}{5}\)

Pipe A fills for 1 hour alone. Pipes A and B work together for 1 hour.

Total filled, \(r*t=W\):
\(W_1=(R_{A}*t_1)+(R_{(A+B)}*t_2)=\)
\((\frac{1}{3}*1)+(\frac{3}{5}*1)=(\frac{1}{3}+\frac{3}{5})=\)

\(\frac{14}{15}\) of R is filled

(2) Time needed to empty that portion?
C drains faster than A and B fill. Subtract combined rate of A and B from rate of C. The result is the rate at which the reservoir empties.

Let T = time needed to drain \(\frac{14}{15}\) of pool

Rate of C = \(\frac{1R}{1hr}\)

\((R_{C}-R_{(A+B)})*T=\frac{14}{15}\)

\((1-\frac{3}{5})*T=\frac{14}{15}\)

\(\frac{2}{5}*T=\frac{14}{15}\)

\(T=(\frac{14}{15}*\frac{5}{2})=\frac{7}{3}\) hrs

\(2\frac{1}{3}\)hrs = \(2\) hrs, \(20\) minutes

A, B, and C work simultaneously at 3 p.m.
2 hours and 20 minutes later is 5:20 p.m.

Answer C
Hope that helps :-)

*3 hours, 45 mins =\(3\frac{3}{4}=\frac{15}{4}\) hours
B, rate:\(\frac{1R}{(\frac{15}{4}hrs)}=(1R*\frac{4}{15}hrs)=\frac{4R}{15hrs}=\frac{4}{15}\)

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A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 11 Oct 2018, 16:40
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Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm


let t=total hours
t/3+(t-1)(4/15)-(t-2)=0
→t=4 1/3 hours
5:20 pm
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A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 13 Oct 2018, 10:09
Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm


Let a,b, c be the rates of 3 pipes. Given -

3(a) = 15/4(b) = 1(c)

a = c/3, b = 4c/15

a(1) + (a+b).1 + (a+b-c).t = 0

t = 2hrs 20 min.

Hence, C.
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Re: A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 13 Oct 2018, 17:33
Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm


The rate of inlet one is 1/3.

The rate of inlet two is 1/(3 + 3/4) = 1/(15/4) = 4/15.

The rate of the outlet is 1/1 = 1.

If we let x = the number of hours since 3:00 pm, then we can create the following equation:

(1/3)(x + 2) + (4/15)(x + 1) - 1x = 0

Multiplying by 15, we have:

5(x + 2) + 4(x + 1) - 15x = 0

5x + 10 + 4x + 4 - 15x = 0

-6x = -14

x = 14/6 = 7/3 hours

Since 7/3 hours = 2 ⅓ hours = 2 hours 20 minutes, the pool reservoir will be empty at 5:20 pm.

Answer: C
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Re: A water reservoir has two inlets and one outlet. Through the inlets wa  [#permalink]

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New post 15 Oct 2018, 22:22
gracie wrote:
Tashin Azad wrote:
A water reservoir has two inlets and one outlet. Through the inlets water reservoir can be filled in 3 hours and 3 hours 45 minutes respectively. Water reservoir can be empties completely in 1 hour by the outlet. If the two inlets are opened at 1:00 pm and 2:00 pm respectively and the outlet at 3:00 pm then the water reservoir will be emptied at?

a) 3:55 pm
b) 5:00 pm
c) 5:20 pm
d) 5:30 pm
e) 5:45 pm


let t=total hours
t/3+(t-1)(4/15)-(t-2)=0
→t=4 1/3 hours
5:20 pm
C



Good job!!!Great approach!!
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Re: A water reservoir has two inlets and one outlet. Through the inlets wa   [#permalink] 15 Oct 2018, 22:22
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