Ginger wants to fill her new swimming pool. She has two pumps; the larger pump takes 40 minutes to fill the pool, and the smaller one takes 60 minutes. How long will it take to fill the pool if both pumps are working?

Question

whpalmer4 · Answer

Think of the volume of the pool as V.  Now write equations to express how much each pump can pump in 1 minute.

Pump 1 can pump V/40 units per minute because after 40 minutes, it will have pumped V units, right?  Similarly, Pump 2 can pump V/60 units per minute because after 60 minutes, it will have pumped V units.  Each minute, the two pumps together will pump V/40 + V/60 units.  Let t be the number of minutes of pumping.  The pumping rate multiplied by t will give us the volume pumped.

$$V = t*(\frac{V}{40}+\frac{V}{60})$$

Now solve that for t and you've got your answer.  Notice that we can divide by sides by V and eliminate it from the equation — we don't need to know how big the pool actually is!