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:

$18 \frac{1}{4}$ hours $19 \frac{1}{2}$ hours $18 \frac{1}{3}$ hours $19 \frac{1}{4}$ hours

$19 \frac{1}{2}$ hours

D+ = 26 hrs, E+ = 78 hrs, ⇒ Time required for D + E to fill the tank completely = \(\frac{78}{3+1}\) = \(\frac{78}{4}\) = $19 \frac{2}{4}$ = $19 \frac{1}{2}$ hours