>If using hose A, I can fill a drum in 20 minutes but if I am going to use hose B, I will only take 18 minutes. If I will use both (A & B), how many minutes will I spend to fill the drum?
>
>30 + 18 = 38; 38/2 = 19, 19/2 = 9.5 which is my answer. Is this correct?

Should not be, because one hose is faster, so they're not contributing halves, but rather proportional shares. Let's see the total filling speed:

v1 (speed of hose A) = 1 drum / 20 minutes= 1/20 d/m
v2 = 1/18 d/m

Total speed= v1+v2= 1/20+1/18=9/180+10/180=19/180

The time needed would be 180/19=9.4736842105

So it's a little faster than you imagined. Just imagine the difference if the second hose was filling the drum in 10 minutes (or don't imagine, calculate it).