Tap A can fill up an empty tank in 3 hours.Tap B can fill up the same empty tank in 4 hours.Tap C can fill up the same empty tank in 6 hours.How many hours will it take to fill up the empty tank if all the taps are turned on at the same time?
If the volume of the tank is, say, V litres, then
A fills it at a rate of V/3 litres/hour
B fills it at a rate of V/4 litres/hour
C fills it at a rate of V/6 litres/hour
So A+B+C would fill it at a rate of V/3 + V/4 + V/6 = 3V/4 litres/hour
Time taken = V/(3V/4) = 4/3 hours or 1hour 20 minutes.
Here's another way I like to do this kind of problem
1/3 + 1/4 + 1/6 =
4/12 + 3/12 + 2/12 =
9/12 Now, take the reciprocal of this fraction
1 + 1/3 hrs