if both crews work together, let's say the finish the job in "t" hours.
so.. in 1 hour, they have done 1/t of the whole work.
now, the new crew, working by itself can do the whole job in 12 hours, that means, in 1 hour, they have done only 1/12 of all the work.
the experienced crew, can do the job in 6 hours, that means in 1 hour, they have done 1/6 of all the work.
now, let's add their rates for 1 hour worth, to see what we get.
[tex]\bf \begin{array}{clclcllll}
\cfrac{1}{12}&+&\cfrac{1}{6}&=&\cfrac{1}{t}\\
\uparrow &&\uparrow &&\uparrow &&\\
new\ crew&&experienced&&total\\
rate/hr&&rate/hr&&work/hr
\end{array}\\\\
-------------------------------\\\\
\textit{let's multiply both sides by \underline{12t}, to toss away the denominators}
\\\\\\
t+2t=12[/tex]
and pretty sure you know how much that is.
