Question

A tank that is filled with water drains at a rate of d216+4d−100 d 2 16 + 4 d − 100 gallons per minute where d is the depth of the tank in feet. Pumping out a tank that is 120 feet deep with this same pump would empty the tank at what rate? 1380 gal/min 1380 gal/min 1280 gal/min 1280 gal/min 900 gal/min 900 gal/min 387.5 gal/min 387.5 gal/min 487.5 gal/min

Answer 1

Given:

Consider the tank that is filled with water drains at a rate of $\dfrac{d^2}{16}+4d-100$ gallons per minute where d is the depth of the tank in feet.

Depth of tank = 120 feet.

To find:

The rate of water drain for that tank.

Solution:

We have, rate of water drain in gallons per minute.

$r=\dfrac{d^2}{16}+4d-100$

where, d is the depth of the tank in feet.

Put d=120, to get the rate of water drain for the tank.

$r=\dfrac{120^2}{16}+4(120)-100$

$r=\dfrac{14400}{16}+480-100$

$r=900+380$

$r=1280$

Therefore, the rate of water drain is 1280 gal/min. Hence, the correct option is B.