Question

A pump can fill a tank in 3 hours. A more powerful pump can fill the same tank in 2 hours. How long would it take to fill the tank with both pumps working?

Answer 1

`\begin{gathered} \text{First Pump}=\frac{1\text{ tank}}{3\text{ hour}}\text{ or a rate of 1/3 tank/h} \\ \text{Second Pump}=\frac{1\text{ tank}}{2\text{ hour}}\text{ or a rate of 1/2 tank/h} \\ \text{If both pumps are working, then add the two rates} \\ (1)/(3)\text{tank/h}+(1)/(2)\text{tank/h}=(5)/(6)\text{tank/h} \\ \text{The new rate is }(5)/(6)\text{tank/h, but since we only one to know the rate of one tank,} \\ \text{we divide both numerator and denominator by }5 \\ ((5)/(5))/((6)/(5))\text{tank/h} \\ \rightarrow(1)/(1.2)\text{tank/h} \\ \text{Which means, that when both pumps are working, it would only take 1.2 hours or} \\ \text{1 hour and 12 minutes} \end{gathered}`