Two pipes a and b can fill an empty cistern in 18 and 27 hours respectively. Pipe c can drain the entire cistern in 45 hours when no other pipe is in operation. Initially, when the cistern was empty pipe a and pipe c were turned on. After a few hours pipe a was turned off and pipe b was turned on instantly. In all, it took 55 hours to fill the cistern. For how many hours was pipe b turned on?
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Answer:
45 hrs
Step-by-step explanation:
Pipe a can fill in 1 hr = 1/18
Pipe b can fill in 1 hr = 1/27
Pipe c can drain in 1 hr = 1/45
Let say for x hrs Pipe a & c were turned on
x(1/18 - 1/45)
=(x/90)(5-2)
= x/30
Now pipe a turned off & pipe b turned on
remaining hrs = 55-x
(55-x) ( 1/27 - 1/45)
= (55-x) (1/135)(5 -3)
= (55-x)2/135
x/30 + (55-x)2/135 = 1
=>(1/270) ( 9x + 220 - 4x) = 1
=> 5x + 220 = 270
=> 5x = 50
=> x = 10
pipe b turned for 55 - 10 = 45 hrs
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