Question

If a tank is emptied in 5 minutes by a pump that is pumping at a rate of 300 gallons per minute ,how long will it take to take to empty the tank with a pump that will pump at a rate of 500 gallons per minute?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{pumping}\mathrm{rate}\mathrm{be}\mathrm{defined}\mathrm{by}\mathrm{w}\mathrm{and}\mathrm{time}\mathrm{taken}\mathrm{to}\mathrm{empty}\mathrm{the}\mathrm{tank} \\ \mathrm{be}\mathrm{denoted}\mathrm{by}\mathrm{t}. \\ \mathrm{where}{\mathrm{t}}_1=5\min ,{\mathrm{t}}_2=?,{\mathrm{w}}_1=300\mathrm{gal}/\min ,{\mathrm{w}}_2=500\mathrm{gal}/\min \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ {\mathrm{t}}_1\times {\mathrm{w}}_1={\mathrm{t}}_2\times {\mathrm{w}}_2 \\ 5\times 300={\mathrm{t}}_2\times 500 \\ {\mathrm{t}}_2=\frac{5\times 300}{500} \\ {\mathrm{t}}_2=3\min \end{gathered}$$
So, it will take 3 mins to empty the tank with a pump that will pump at a rate of 500 gallons per minute