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?

1 Answer
May 3, 2016

t=36" minutes"

Explanation:

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"
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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"