It is given that the two pipes fill the storage tank in 9 hours. The smaller pipe takes 3 times as long to fill the pipe as the larger pipe.
Let the time taken by the larger pipe be X, the time taken by the smaller pipe is 3*X. The rate at which the tank is filled by the larger pipe is `1/X` and the rate at which it is filled by the smaller pipe is `1/(3X)` . The rate at which both the pipes together fill the tank is `1/X + 1/(3X) = 4/(3X)` .
The time it takes the pipes to fill the tank is `(3X)/4` .
`(3X)/4 = 9`
=> X = `(9*4)/3`
=> X = 12
It would take the larger pipe alone 12 hours to fill the tank.
Let t be the time to fill the tank by larger pipe and x the capacity of the tank in litres
The time taken to fill the tank by smaller pipe = 3t
flow rate of larger pipe = x/t litre/hour
flow rate of smaller pipe = x/3t litre/hour
combined capacity of the two pipes = x/t +x/3t = 4x/3t litre/hour
Time required to fill the tank of capacity x using combime capcity of both pipes= x/(4x/3t) = 3t/4 hours
Time required to fill the tank by both pipes = 9 hours (given)
3t/4 = 9 hours
t = 9*4/3 = 12 hours
Time taken by the larger pipe alone to fill the tank is 12 hours