Filling a settling pond

Question

A sewage treatment plant has two inlet pipes to its settling pond. One pipe can fill the pond 3 times as fast at the other pipe, and together they can fill the pond in 12 hr. How long will it take the faster pipe to fill the pond alone?

 

Answer 1

V= volume of the pond

 

V= x. t1   x=flow rate of slow pipe, t1= time that slow pipe needs to fill the pond

 

V= y. t2    x=flow rate of fast pipe, t2= time that fast pipe needs to fill the pond

 

y=3x

 

V= (x+y).12= 4x.12=48x

 

x= V/48

 

for fast pipe

 

V=3.V.t2/48

 

t2=48/3=16hr