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?

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» <html><body><p>Let VT be volume of tank</p><p></p><p>Let tA be the time for <a href="https://interviewquestions.tuteehub.com/tag/pipe-1154875" style="font-weight:bold;" target="_blank" title="Click to know more about PIPE">PIPE</a> A to fill tank</p><p></p><p>Let tB be the time for pipe <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> to empty tank</p><p></p><p>Pipe A flow <a href="https://interviewquestions.tuteehub.com/tag/rate-1177476" style="font-weight:bold;" target="_blank" title="Click to know more about RATE">RATE</a> = VT / tA</p><p></p><p>Pipe B flow rate = -VT / tB</p><p></p><p>Net flow rate:</p><p></p><p>RN = (VT / tA) - (VT / tB) = (VTtB - VTt) / (tAtB)</p><p></p><p>= VT(tB - tA) / tAtB</p><p></p><p>Flow rate, R = <a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a> / t</p><p></p><p>t = V / R</p><p></p><p>t = ttot</p><p></p><p>R = RN</p><p></p><p>V = VT</p><p></p><p>ttot = VT / RN = VT / (VT(tB - tA) / tAtB) = tAtB / (tB - tA)</p><p></p><p>tA = 6 hrs</p><p></p><p>tB = 9 hrs</p><p></p><p>ttot = 6 x 9 / (9 - 6) = 18 hrs</p></body></html>