A pipe A fill pipe B takes 3 hours more than pipe A to do the same work Find the part of cistern filled by pipes A and B in one hour The two pipes can together fill it in 6 hours 40 minutes Frame the correct equation Solve for x and find the time taken by each pipe to fill the cisternsamthe cistern in x hours and
Answers
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
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour
=
1
5
part filled by pipe B in 1 hour =
1
6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour
=
1
12
Net part filled by Pipes A,B,C together in 1 hour
=
1
5
+
1
6
−
1
12
=
17
60
i.e., the tank can be filled in
60
17
=
3
9
17
hours