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?

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

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