Question 1207781
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A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. 
With both faucets closed and the stopper removed, the tub will empty in 20 minutes. 
How long will it take for the tub to fill if both faucets are open and the stopper is removed?
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Your equation is incorrect.


<pre>
In this problem, there are two opposite processes.

One process is filling with the rate of  {{{1/15}}}  of the volume per minute
(two faucets combined).


Another process is draining with the rate  {{{1/20}}}  of the volume per minute.


So, when both facets are open and the stopper is removed, the net filling rate is the difference 

    {{{1/15}}} - {{{1/20}}} = {{{4/60}}} - {{{3/60}}} = {{{1/60}}}  of the volume per minute.


It means that the filling process will take 60 minutes, or 1 hour.    <U>ANSWER</U>
</pre>


Thus, the problem is just solved (mentally).



If you want to write an equation, you should formalize this reasoning.



<pre>
Let "t" be the time to fill, in minutes.


Then in t minutes, the two facets will fill  {{{t/15}}}  part of the volume,
while through the stopper hole, the  {{{t/20}}} part of the volume will be removed.


The volume will be fully filled when

    {{{t/15}}} - {{{t/20}}} = 1   (the whole volume).


Write with common denominator and find t

    {{{(4t)/60}}} - {{{(3t)/60}}} = 1,

    {{{t/60}}} = 1,

    t = 60*1 = 60 minutes.


<U>ANSWER</U>.  The required time is 60 minutes,  or 1 hour.
</pre>

Solved.


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