Question

Two pipes running together can fill a cistern in `3 1/13` 
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern. 

Answer 1

Let one pipe fills the cistern in x mins.
Therefore, the other pipe will fill the cistern in `(x+3)`mins.  

Time taken by both, running together, to fill the cistern =`3 1/13  min s=40/13  min s` 

Part filled by one pipe in 1 min=`1/x` 

Part filled by the other pipe in 1 min =`1/(x+3)`  

Part filled by both pipes, running together, in 1 min =`1/x+1/(x+3)` 

∴ `1/x+1/(x+3)=1/40` 

⇒ `((x+3)+x)/(x(x+3))=13/40` 

⇒`(2x+3)/(x^2+3a)=13/40` 

⇒`13x^2+39x=80x+120` 

⇒`13x^-41x-120=0` 

⇒`13x^2-(65-24)x-120=0` 

⇒`13x^2-65x+24x-120=0` 

⇒`13x(x-5)+24(x-5)=0` 

⇒`(x-5)(13x+24)=0` 

⇒`x-5=0  or  13x+24=0` 

⇒`x=5  or  x=--24/13` 

⇒`x=5` ( ∵ Speed cannot be a negative fraction)
Thus, one pipe will take 5 mins and other will take{(5+3)=8}mins to fill the cistern.