The time (t) required to empty a tank varies inversely as the rate (r) of pumping. A pump can empty a tank in 90 minutes at the rate of 1200 L/min. How long will the pump take to empty the tank at 3000 L/min?

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Answer 1 · 2016-05-03T12:33:26

#t=36" minutes"#

#color(brown)("From first principles")#

90 minutes at 1200 L/min means that the tank holds #90xx1200 L#

To empty the tank at a rate of 3000 L/m will take the time of

#(90xx1200)/3000 = (108000)/3000 = 36" minutes"#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Using the method implied in the question")#

#t" "alpha" "1/r" "=>" "t=k/r" "#where k is the constant of variation

Known condition: #t=90" ; "r=1200#

#=>90=k/1200=> k=90xx1200#

So #t=(90xx1200)/r#

Thus at #r=3000# we have

#t=(90xx1200)/(3000)#

Observe that this is exactly the same as in first principles.

#t=36" minutes"#