Question

one hose can fill a small swimming pool in 55 minutes a larger hose can fill the pool in 45 minutes how long will it take the two hoses to fill the pool working together?

Answer 1

J in 55min

J in 45min ( bigger hose)

`\begin{gathered} (1)/(55)+(1)/(45) \\ (45(1)+55(1))/(55(45)) \\ (100)/(2475) \\ \text{Take the reciprocal} \\ (2475)/(100) \\ 24.75\text{ minutes} \end{gathered}`

Alternative method

The trick is to convert the numbers you are given to numbers that you can add together.

You have minutes per pool. You can’t work with that. But if you take the reciprocal of each you get pools per minute.

So if the first hose fills 1/55 = 0.01818 pools per minute and the second one fills 1/45 = 0.0222 pools per minute, then both of them will fill 0.1818 + 0.0222 = 0.04040 pools per minute. If we take the reciprocal of that we end up with 1/0.04040 = 24.75 minutes per pool.