SOLUTION: a fish pond can be filled by an inlet pipe in twelve hours if an outlet pipe is opened. If the pipe was allowed to run alone for two whole hours, after which the outlet pipe was op

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a fish pond can be filled by an inlet pipe in twelve hours if an outlet pipe is opened. If the pipe was allowed to run alone for two whole hours, after which the outlet pipe was op      Log On


   

Question 760010: a fish pond can be filled by an inlet pipe in twelve hours if an outlet pipe is opened. If the pipe was allowed to run alone for two whole hours, after which the outlet pipe was opened, it would take the inlet pipe for more hours to fill up the pond. How long would it take the inlet pipe alone to fill the tank full from start to finish with the outlet pipe removed?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
f for fill, e for empty. Those are rates in FillThePool per Hour.
f%3Ee.

f%2Be=1%2F12

Inlet pipe runs by itself for 2 hours, then f%2A2 is how much FillThePool is done in that time.
The outlet pipe is opened and with both pipes opened this way, 4 hours was needed to finish filling the pool: This amount of FillThePool was %281%2F12%29%2A4
Put the two amounts of FillThePool together because their sum is 1 FillThePool.
2f%2B%281%2F12%29%2A4=1
Solve for f.
2f=1-%281%2F12%29%2A4
2f=1-1%2F3=3%2F3-1%2F3
2f=2%2F3
highlight%28f=1%2F3%29

That is 1 job in 3 hours. This means (1/3) jobs per hour or:
ANSWER: The inlet pipe fills the pool in THREE hours if the outlet pipe is closed.