two pipes running together can fill a tank in 3 1/13 hours if one takes 3 hours more than the other to fill the tank then how much time will it take to fill the tank
Answers
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 the cistern, what is the time in which each pipe would fill the cistern?
Let the volume of the cistern be V.
Together two pipes take 3 1/13 mins = 40/13
Rate of both the pipes together = V/(40/13)
Let pipes be A and B,
Time taken by A = t mins , So rate = V/t
Time taken by B = t+3 mins, So rate = V/(t+3)
Combined rate = V/t + V/(t+3)
We already know that combined rate = V/(40/13)
Equating both ,
V/t + V/(t+3) = V/(40/13)
1/t + 1/(t+3) = 13/40
(t+3+t) / t(t+3) = 13/40
(2t + 3)/ (t^2+3t) = 13/40
80t + 120 = 13t^2 + 39t
13t^2 - 41t - 120 = 0
The quadratic equation yields two roots :
5 and -1.846 , since time cannot be negative
Time taken by pipe A = 5 mins
Time taken by pipe B = 5+3 = 8 mins