Question 760010
f for fill, e for empty.  Those are rates in FillThePool per Hour.
{{{f>e}}}.


{{{f+e=1/12}}}


Inlet pipe runs by itself for 2 hours, then {{{f*2}}} is how much FillThePool is done in that time.

The outlet pipe is opened and with both pipes opened this way, 4 hours was needed to finish filling the pool:  This amount of FillThePool was {{{(1/12)*4}}}

Put the two amounts of FillThePool together because their sum is 1 FillThePool.
{{{2f+(1/12)*4=1}}}
Solve for f.

{{{2f=1-(1/12)*4}}}
{{{2f=1-1/3=3/3-1/3}}}
{{{2f=2/3}}}
{{{highlight(f=1/3)}}}


That is 1 job in 3 hours.  This means (1/3) jobs per hour or:
ANSWER: The inlet pipe fills the pool in THREE hours if the outlet pipe is closed.