SOLUTION: An outlet pipe can empty a cistern in 18 hours. With cistern full, this pipe and a second pipe are opened and together they empty 3/5 of the cistern in 6 hours. If the first pipe i

Question 746639: An outlet pipe can empty a cistern in 18 hours. With cistern full, this pipe and a second pipe are opened and together they empty 3/5 of the cistern in 6 hours. If the first pipe is then shut off, how long will it take the second pipe to finish emptying the cistern?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An outlet pipe can empty a cistern in 18 hours.
With cistern full, this pipe and a second pipe are opened and together they empty 3/5 of the cistern in 6 hours.
If the first pipe is then shut off, how long will it take the second pipe to finish emptying the cistern?
:
Let t = time required by the 2nd pipe to empty the cistern
Let the completed job = 1 (An empty cistern)
:
"this pipe and a second pipe are opened and together they empty 3/5 of the cistern in 6 hours."
+ =
Multiply by 90t, resulting in:
5t(6) + 90(6) = 18t(3)
30t + 540 = 54t
540 = 54t - 30t
540 = 24t
t = 540/24
t = 22.5 hr for the 2nd pipe to empty the cistern alone
:
"If the first pipe is then shut off, how long will it take the second pipe to finish emptying the cistern"
Let f = time required for 2nd pipe to finish emptying the cistern
+ = 1
multiply by the least common multiple of 18 and 22.5, 405, resulting in:
22.5(6) + 18(f+6) = 405
135 + 18f + 108 = 405
18f = 405 - 135 - 108
18f = 162
f = 162/18
f = 9 more hrs to finish

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