so. the smaller hose, can fill the pool in 8hrs
in 1hr then, it really has done only 1/8 of the job
if we take the filled pool to be the total job time, or "t"
then the smaller hose in 1hr has only done only 1/8 in "t" amount or [tex]\bf \cfrac{1}{8}t[/tex]
now, the bigger hose, can do the filling in 6hrs
that means in 1hr, it has only done then 1/6 in "t" time or [tex]\cfrac{1}{6}t[/tex]
now, the whole job, is a whole, or 1
so.. let us add those rates of each hose together, to see how long they'd take [tex]\bf \cfrac{1}{8}t+\cfrac{1}{6}t=1\implies \cfrac{t}{8}+\cfrac{t}{6}=1[/tex]
solve for "t"
