Pipe P can fill a tank alone in 7 hours. Pipe Q can fill the same tank alone in 13 hours. In how much time can they together fill the tank?

P  = 7 hrs

Q =13 hrs

Total work = lcm (7,13)= 91 hrs

P's effiency = $$91\div7$$ =13

Q's effiency = $$91\div13$$ =7

(P+Q)'s together takes  = $$Total work\div total efficency$$

                                    = $$91\div20$$

convert 91 hrs into minutes = $$91\times 60=5460$$   

                                    = $$5460\div20$$

                                   = 273 min

                                   = $$273\div60$$

                                    =4 hours 33 minutes