pipe a can fill a tank in 6 hours but another pipe B can empty it in 9

1.	pipe a can fill a tank in 6 hours but another pipe B can empty it in 9 hours. if both pipes are opened together ,then how much time will it take to fill the tank?
Answer» Let VT be volume of tank Let tA be the time for PIPE A to fill tank Let tB be the time for pipe B to empty tank Pipe A flow RATE = VT / tA Pipe B flow rate = -VT / tB Net flow rate: RN = (VT / tA) - (VT / tB) = (VTtB - VTt) / (tAtB) = VT(tB - tA) / tAtB Flow rate, R = V / t t = V / R t = ttot R = RN V = VT ttot = VT / RN = VT / (VT(tB - tA) / tAtB) = tAtB / (tB - tA) tA = 6 hrs tB = 9 hrs ttot = 6 x 9 / (9 - 6) = 18 hrs

pipe a can fill a tank in 6 hours but another pipe B can empty it in 9 hours. if both pipes are opened together ,then how much time will it take to fill the tank?

Answer»

Let VT be volume of tank

Let tA be the time for PIPE A to fill tank

Let tB be the time for pipe B to empty tank

Pipe A flow RATE = VT / tA

Pipe B flow rate = -VT / tB

Net flow rate:

RN = (VT / tA) - (VT / tB) = (VTtB - VTt) / (tAtB)

= VT(tB - tA) / tAtB

Flow rate, R = V / t

t = V / R

t = ttot

R = RN

V = VT

ttot = VT / RN = VT / (VT(tB - tA) / tAtB) = tAtB / (tB - tA)

tA = 6 hrs

tB = 9 hrs

ttot = 6 x 9 / (9 - 6) = 18 hrs