Question 1208808
.
A tub can be filled with hot water in 18 minutes, or with cold water in 12 minutes. 
The tub can also be emptied when the plug is pulled out, in 9 minutes. 
Farley ran the hot water in his tub for 8 minutes, 
then both the cold and hot water together for 2 minutes, 
and then with the two taps still running, he accidentally pulled the plug. 
How long did it take, in minutes, for the tub to fill after the plug was pulled?
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<pre>
The rate of filling the tub with the hot water is  {{{1/18}}}  of the tube volume per minute.

The rate of filling the tub with the cold water is  {{{1/12}}}  of the tube volume per minute.

The rate of draining the tub is  {{{1/8}}}  of the tube volume per minute.


The rate of filling the tube in the first 8 minutes was  {{{1/18}}}  of the tube volume per minute.

The rate of filling the tube in the next 2 minutes was  {{{1/18+1/12}}} = {{{2/36 + 3/36}}} = {{{5/36}}}  of the tube volume per minute.

The net rate of filling the tube in the last t minutes was  {{{1/18+1/12-1/9}}} = {{{2/36 + 3/36-4/36}}} = {{{1/36}}}  of the tube volume per minute.


An equation to fill the tube under given conditions is

    {{{8/18}}} + {{{2*(5/36)}}} + {{{t*(1/36)}}} = 1.


Simplify and find t

    {{{(2*8)/36}}} + {{{10/36}}} + {{{t/36}}} = 1,

    {{{(16 + 10 + t)/36}}} = 1,

    26 + t = 36,

    t = 36 - 26 

    t = 10.


<U>ANSWER</U>. It took 10 minutes to fill the tub after the plug was pulled.
</pre>

Solved.


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