Two pipes, D and E, can fill a cistern in 26 and 78 hours, respectively, while working alone. If the two pipes are opened together, the time taken to fill the cistern is:

A

$$18\frac{1}{4}$$ hours

B

$$19\frac{1}{2}$$ hours

C

$$18\frac{1}{3}$$ hours

D

$$19\frac{1}{4}$$ hours