Two pipes running together can fill in 2 8/11 mins.If one pipe takes 1min more than other tofill the cistern?

Question

Find the time in which each pipe would fill the cistern.

Answer 1

Let t= time for pipe #1

1+t = time for pipe #2

Then their rate per min. (The portion of the tank filled in one min)

Rate(1) = 1/t

Rate(2)= 1/(t+1)

If the tank is filled by both pipes in 2 8/11 min = 30/11 min The portion of the tank filled in one min. is 1/(30/11) = 11/30

We will get our equation by looking at what happens in one minute, their rates.

1/t + 1/(t+1) = 11/30

(t+t+1)/(t(t+1)) = 11/30

60t + 30 = 11t^2 + 11t

11t^2 -49t -30 = 0

(11t + 6)(t - 5)= 0

The appropriate solution is t = 5 for pipe #1 and 6 min. for pipe #2