If Person A can deliver papers in 40 min, and person B can do the same papers in 50 min, how long does it take when they work together?
This is a rational expression problem. Is there an easy, or not complicated way to do this?
$\dfrac1{40} + \dfrac1{50} = \dfrac1x $
It didn't work this way though. It did for a different problem. Why must I keep changing the format? Why can't this format work?
Consider $P$ the amount of papers. In one minute the first person delivers $\frac{P}{40}$, the second one $\frac{P}{50}$. Together in one minute they deliver $\frac{P}{40}+\frac{P}{50}$. So they need
$$\frac{P}{ \frac{P}{40}+\frac{P}{50}}$$ minutes to deliver the whole thing.
The quantity $P$ magically disappears...