pipe can fill a cistern 8 hrs and another 10 hrs.both are opened at same time.if 2nd is closed 2 hrs before the cistern is filld up

Answer 1

pipe can fill a cistern 8 hrs and another pipe 10 hrs.both are opened at same time.if 2nd is closed 2 hrs before the cistern is filled up.find in what time,the cistern will be filled up?

Answer 2

rate of first pipe = 1/8
rate of 2nd pipe = 1/10
combined rate = 1/8 + 1/10 = 9/40

let the time taken to fill it be t hours

(t-2)(9/40) + 2(1/8) = 1 <----- the whole cistern
(9/40)t - 9/20 + 1/4 = 1
times 40
9t - 18 + 10 = 40
9t = 48
t = 48/9 hrs or 5 1/3 hrs

check:
3 1/3 hrs times 9/40 + 2 times 1/8
= (20/9)(9/40) + 2(1/8)
= 1