SOLUTION: The Northern Hills swimming pool can be filled by a vent in 10 hours. It can emptied by a drain pipe in 20 hours. The manager mistankely leaves the drain pipe open while trying to

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The Northern Hills swimming pool can be filled by a vent in 10 hours. It can emptied by a drain pipe in 20 hours. The manager mistankely leaves the drain pipe open while trying to       Log On


   

Question 284124: The Northern Hills swimming pool can be filled by a vent in 10 hours. It can emptied by a drain pipe in 20 hours. The manager mistankely leaves the drain pipe open while trying to fill the pool before memorial day, How long will it take to fill the pool.
Found 2 solutions by solver91311, oberobic:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Working together problems go like this:

If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period.

So, working together, they can do



of the job in 1 time period.

Therefore, they can do the whole job in:



time periods.

But you have a problem where you have two things working against one another, so the first calculation becomes:



And the second part becomes:




John

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The vent fills the pool in 10 hours, so it fills at a rate of 1/10 of the job per hr.
The drain empties the pool in 20 hours , so it drains at a rate of -1/20 per hr.
We can imagine the pool being full as = 1.
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x(1/10) -x(1/20) = 1 job
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Multiply through by 20.
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2x - x = 20
x = 20
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Checking, we can find how much water was put in vs. how much water was pulled out.
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20 hr * 1/10 per hr = 2 :: So in 20 hrs the pool can be filled twice.
20 hr * 1/20 per hr = 1 :: So in 20 hrs the pool can be drained once.
2-1 = 1, which suggests the pool is full at that instant.
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But I suspect the pool cannot hold twice it's normal volume. That is, once you have it full, adding more water just flows over the rim and floods the building. So, perhaps 20 hrs is too long.
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Perhaps a better model is to suggest the pool is filling and draining simultaneously. That means it fills at a net rate of 1/10 - 1/20 per hr.
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x(1/10-1/20) = 1
x(1/20) = 1
x = 20
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Hmmm...20 again.
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So, the answer is 20 hrs.
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But, after 20 hrs the pool will be flooding the building since it will still be adding water at the rate of 1/10 the volume of the pool per hr minus 1/20 of the volume per hr or a net rate of 1/20 of the volume per hr.
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Done.