Work, cistern, pipe?

Question

Pipes A and B can fill/empty a cistern in 7 hours and 3 hours respectively. if Both A and B are inlets, and Pipe C empties the cistern in 5 hours, then all the three together can fill the cistern in how many hours?

Answer 1

A fill/empty in 7 hours

B=fill/empty in 3 hours

c= in 5 hours

if A,B are inlets

C=outlet

suppose if u take the volume of the cistern is= 105  

why 105 ?. because it should by divided by all the values (7,3,5)

so volume = 105

if A takes 7 hours that means

flow rate of A = 105/7 =15 liters/hour

flow rate of B=105/3= 35 liters/hour

flow rate of C = 105/5 =21 liters/hour

so if u add A,B (because A,B working together as inlet, and subtract C (because C is going out)

inlet= 35+15=50 liters

Outlet=21

total flow  =50-21=29 liters/hour

so we need 105 liters

so 105 liters/29(liters/hour)  = 3.6206897 hours

the final time required when three A,B,C working is  =  3.6206897 hours to fill the cistern