# 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?

May 3, 2016

$t = 36 \text{ minutes}$

#### Explanation:

$\textcolor{b r o w n}{\text{From first principles}}$

90 minutes at 1200 L/min means that the tank holds $90 \times 1200 L$

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

$\frac{90 \times 1200}{3000} = \frac{108000}{3000} = 36 \text{ minutes}$
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$\textcolor{b r o w n}{\text{Using the method implied in the question}}$

$t \text{ "alpha" "1/r" "=>" "t=k/r" }$where k is the constant of variation

Known condition: $t = 90 \text{ ; } r = 1200$

$\implies 90 = \frac{k}{1200} \implies k = 90 \times 1200$

So $t = \frac{90 \times 1200}{r}$

Thus at $r = 3000$ we have

$t = \frac{90 \times 1200}{3000}$

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

$t = 36 \text{ minutes}$