now let's say hmmm
p1 = pipe1 p2 = pipe2 and p3 = pipe3
so, we know p1 can do the whole shebang in 45hours
that simply means, that in 1hr, percentage wise, p1 can do really (1/45)th of the job
ok... now, if we have p1 and p2 working together, they can do the whole thing in 30hrs, so, in 1hr, they both working, have done only (1/30)th of the job, so, what's p2's rate? well
[tex]\bf \begin{array}{clclclll}
\cfrac{1}{45}&+&\cfrac{1}{p2}&=&\cfrac{1}{30}\\
\uparrow &&\uparrow &&\uparrow \\
\textit{p1's rate/hr}&&\textit{p2's rate/hr}&&\textit{both's rate/hr}
\end{array}\\\\
-----------------------------\\\\
\cfrac{1}{p2}=\cfrac{1}{30}-\cfrac{1}{45}\implies \cfrac{1}{p2}=\cfrac{1}{90}\implies \boxed{90=p2}[/tex]
that simply means, p2 can do the whole job in 90 hours... notice, 90 is 45*2, that just means p2 is twice as slow as p1
now.. we know p2 and p3 working together can do the job in 40hrs, what's p3's rate?
well [tex]\bf \begin{array}{clclclll}
\cfrac{1}{p3}&+&\cfrac{1}{90}&=&\cfrac{1}{40}\\
\uparrow &&\uparrow &&\uparrow \\
\textit{p3's rate/hr}&&\textit{p2's rate/hr}&&\textit{both's rate/hr}
\end{array}\\\\
-----------------------------\\\\
\cfrac{1}{p3}=\cfrac{1}{40}-\cfrac{1}{90}\implies \cfrac{1}{p3}=\cfrac{1}{72}\implies \boxed{72=p3}[/tex]
so p3, can do the whole shebang in 72hrs then
