Working rate problem > Working alone at its constant rate, machine A takes 3 hours to pro- duce a batch of identical computer parts. Working alone at its constant rate, ma- chine B takes 2 hours to produce an identical batch of parts. How long will it take the two machines, working simultaneously at their respective constant rates, to pro- duce an identical batch of parts? The rate of work is clearly $\frac12$ and $\frac13$ . Now how to balance this equation?

for A for 1 hour it can produce $1/3$ batch of parts

for B for 1 hour it can produce $1/2$ batch of parts

for A+B for 1 hour they can produce 1/3 + 1/2 $ = $5/6$ batch of parts

so to produce 1 batch they need $6/5$ hours so they need 72 minutes

hope its clear