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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