Question

Two pipes running together can fill a cistern in 31/3 min. if one pipe takes 3 minutes more than the other to fill it, then find the time in which each pipe would fill the cistern

Answer 1

Answer:

Step-by-step explanation:

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