# Two pipes fill a storage tank in 9 hours. The smaller pipe takes 3 times as long to fill the pipe as the larger pipe. How long would it take the larger pipe alone to fill the tank?

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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*