Question

IF pumping out a mine that is $D$ feet deep required a pump that pumps a minimum of $\frac{D^2}{25}+4D-250$ gallons per minute, pumping out a mine that is $150$ feet deep would require a pump that pumps a minimum of how many gallons per minute?

• A. $362$
• B. $500$
• C. $800$
• D. $1,250$
• E. $1,750$

Answer 1

The correct option is D $1,250$

A pump pumps $\frac{D^2}{25}+4D-250$ gallons per minutes

Where $D=$ depth

According to the question $D=150$ feet

$\therefore$ Pump pumps a minimum $=$ $\frac{(150{)}^2}{25}+4\times 150-250$

$\Rightarrow \frac{22500}{25}+600-250$

$\Rightarrow 900+600-250$

$\Rightarrow 1500-250=1250$ gallons/minute