A pipe can fill a tank in 2\frac{2}{3} hours, and another pipe empties it in 4 hours. If both are opened together, how long will it take to fill the tank?

Time taken by filling pipe = $2\frac{2}{3}$ hours

$2\frac{2}{3} = \frac{8}{3}$ hours

Filling rate of pipe A:

$= \frac{1}{8/3} = \frac{3}{8}$ tank per hour

Emptying rate of pipe B:

$= \frac{1}{4}$ tank per hour

Net filling rate when both are opened:

$= \frac{3}{8} - \frac{1}{4}$

$= \frac{3}{8} - \frac{2}{8}$

$= \frac{1}{8}$ tank per hour

Time to fill the tank:

$= \frac{1}{1/8} = 8$ hours

Answer: 8 hours