A tank can be filled in 9 hours and drained in 11 hours. How long will it take to fill if the drain is left open?

## A tank can be filled in 9 hours and drained in 11 hours. How long will it take to fill if the drain is left open?

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# 4 Answers

rate *time=output

t=time

rate of fill *t=Volume of tank (filled)

rate of fill*9=V

rate of fill=V/9

rate of drain*t=Volume of tank(drained)

rate of drain*11=V

rate of drain=V/11

time needed to fill the tank with both drains open:

[(V/9)-(V/11)]*t=V

[(1/9)-(1/11)]*t=1

(2/99)*t=1

t=99/2 or 49.5 hrs

check: (99/2)*(1/9)=11/2=5 1/2 tanks filled

(99/2)*(1/11)=9/2=4 1/2 tanks drained

difference is 1 tank filled

After 9 hours 9/11 of the tank will be drained, so 2/11 will be filled. Since you need to fill 1 tank, you will have to repeat 9-hour cycle 11/2=5.5 times, that is, total time required to fill the tank is 9*11/2=49.5 hours.

Let's assume that

Let's mark work, which must be done as

Productivity of the pipe-A is

Productivity of the pipe-B is

Tank fill rate is:

(1/9) - (1/11) = 2/99

**fills the tank, and***pipe-A***drains the tank.***pipe-B*Let's mark work, which must be done as

*"1"*Productivity of the pipe-A is

*1*/9 (unit per hour)Productivity of the pipe-B is

*1*/11 (unit per hour)Tank fill rate is:

(1/9) - (1/11) = 2/99

*1*รท (2/99) = 99/2 =**(hours)***49.5*What we know:

It fills up faster than it drains

Variables:

X

_{f}= amount of liquid in a full tank (units do not matter, pick one)Equations:

x

_{fill}(t)=(X_{f}/9)tx

_{fill}(0)=0x

_{fill}(9)=X_{f}m=(X

_{f}/9)x

_{empt}(t)=(-X_{f}/11)t_{ }x

_{empt}(0)=X_{f}x

_{empt}(11)=0m=(-X

_{f}/11)Solve:

x

_{total}(t)=x_{fill}(t) + x_{empt}(t)= (X

_{f}/9)t + (-X_{f}/11)t= (11X

_{f}/99)t - (9X_{f}/99)t_{ }= (2X

_{f}/99)tset x

_{total}(t)=X_{f}X

_{f}= (2X_{f}/99)t**t=99/2**

Check:

Choose full tank = 1

xfill(t)=(1/9)t

xfill(0)=0

xfill(9)=1

m=(1/9)

xempt(t)=(-1/11)t

xempt(0)=1

xempt(11)=0

m=(-1/11)

xfill(0)=0

xfill(9)=1

m=(1/9)

xempt(t)=(-1/11)t

xempt(0)=1

xempt(11)=0

m=(-1/11)

xtotal(t)=xfill(t) + xempt(t)

= (1/9)t + (-1/11)t

= (11/99)t - (9/99)t

= (2/99)t

set xtotal(t)=1

1 = (2/99)t

= (1/9)t + (-1/11)t

= (11/99)t - (9/99)t

= (2/99)t

set xtotal(t)=1

1 = (2/99)t

**t=99/2** *Edit

WHOOPS! I forgot to divide

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