SOLUTION: Please help me with this problem. I think it needs to be set up as a linear equation. Also, it would help if you could explain it step by step for me. Thanks so much! ** An empty s

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Question 30847: Please help me with this problem. I think it needs to be set up as a linear equation. Also, it would help if you could explain it step by step for me. Thanks so much! ** An empty swimming pool can be filled in 10 hours. When full, the pool can be drained in 16 hours. How long will it take to fill the pool if the drain is left open?
Found 2 solutions by venugopalramana, Nate:
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
Please help me with this one. ** An empty swimming pool can be filled in 10 hours.
SO IN 1 HOUR WE CAN FILL 1/10 POOL
When full, the pool can be drained in 16 hours.
SO IN 1 HOUR 1/16 POOL WILL BE DRAINED
How long will it take to fill the pool if the drain is left open?
SO IN 1 HOUR 1/10 - 1/16 = (8-5)/80 = 3/80 POOL WILL BE FILLED
SO IT TAKES 80/3 = 26.67 HRS TO FILL THE POOL

Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
work is the product of the rate and time
RATE:
the pipe can fill the pool in 10 hours *has to be in fraction, so it is a ratio of 1/10*
the drainer can drain the pool in 16 hours *has to be in fraction, so it is a ratio of -1/16*
TIME:we have to find the time; let us define time as 't'
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RATE*TIME=WORK
pipe = t/10
drainer = -t/16
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it takes one job, so:
t/10 - t/16 = 1
(t/10 - t/16 = 1)80 multiply by lowest common multiple
8t - 5t = 80
3t = 80
t = 80/3
t = 26 and 2/3 hours to fill the pool