Question:
Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?
Solution:
A can fill a tank in 10 hours.
B can fill a tank in 15 hours.
Pipe A fills $\frac{1}{10}$ of the tank in one hour.
Pipe B fills $\frac{1}{15}$ of the tank in one hour.
Part of tank filled by pipes A and B together $=\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6}$
Thus, pipes A and B require 6 hours to fill the tank.