SOLUTION: Word problem. It takes 60 minutes to fill a pond with water alone. It takes 80 minutes to drain a pond of water alone. How long will it take to fill the pond while it is bei

Algebra ->  Expressions-with-variables -> SOLUTION: Word problem. It takes 60 minutes to fill a pond with water alone. It takes 80 minutes to drain a pond of water alone. How long will it take to fill the pond while it is bei      Log On


   

Question 436132: Word problem.
It takes 60 minutes to fill a pond with water alone.
It takes 80 minutes to drain a pond of water alone.
How long will it take to fill the pond while it is being drained at the same time?
Found 3 solutions by mananth, ikleyn, josgarithmetic:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
consider filling or emptying the pool as 1 job.
emptying the pool = 80 minutes
so 1/80 of the job is done in 1 minute
...
Filling time = 60 minutes
1/60 of the job in 1 minute
..
difference = 1/60 -1/80
(80-60)/80*60
20/2400
1/120 of the job is done in 1 minute when both are on.
so it will take 120 minutes to fill the pool.

Answer by ikleyn(53570) About Me  (Show Source):
You can put this solution on YOUR website!
.
Word problem.
It takes 60 minutes to fill a pond with water alone.
It takes 80 minutes to drain a pond of water alone.
How long will it take to fill the pond while it is being drained at the same time?
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        The solution in the post by @mananth is  FATALLY  WRONG  due to elementary arithmetic error.
        I came to bring a correct solution.


consider filling or emptying the pool as 1 job.
emptying the pool = 80 minutes
so 1/80 of the job is done in 1 minute
...
Filling time = 60 minutes
1/60 of the job in 1 minute
..
difference = 1/60 -1/80
(80-60)/80*60
20/4800
1/240 of the job is done in 1 minute when both are on.
so it will take 240 minutes = 4 hours to fill the pool.

Solved correctly.


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It can be seen even with unarmed eye, using common sense - ONLY.

The filling hose fills the tank in 1 hour - but then the drain takes out 3/4 of the water
from the tank during this 1 hour,
so only 1/4 of the tank is filled in one hour.

Hence, 4 hours are needed.



Answer by josgarithmetic(39720) About Me  (Show Source):
You can put this solution on YOUR website!
               rate         time        amount

filling        1/60         60           1

draining       1/80         80           1

combined    1/60-1/80        x           1

The rates are additive, but need to understand draining is negative while filling is positive.
1%2F60-1%2F80 ponds per minute
4%2F240-3%2F240
1%2F240
That is 1 pond in 240 minutes, or 240 minutes to fill the 1 pond with both flows opened.