Question:
Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened together?
Solution:
Time taken by tap A to fill the tank $=6$ hours
Time taken by tap B to fill the tank $=8$ hours
Time taken by tap C to fill the tank $=12$ hours
A fills $\frac{1}{6}$ of the tank in one hour.
B fills $\frac{1}{8}$ of the tank in one hour.
C fills $\frac{1}{12}$ of the tank in one hour.
Part of the tank filled in one hour using all the three pipes $=\frac{1}{6}+\frac{1}{8}+\frac{1}{12}=\frac{4+3+2}{24}=\frac{9}{24}$
Time taken by A, B and C together to fill the tank $=\frac{24}{9}=\frac{8}{3}=2 \frac{2}{3}$ hours