There are two inlets and one outlet to a cistern. One of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:00AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?	Choices:  A) 2 hours  B) 2.5 hours  C) 3 hours  D) 3.5 hours  E) 4 hours
The combined inflow rate of the two inlets is 1/2 + 1/4 = 3/4 cistern/hour. Thus, working together, it takes 4/3 hours (time is reciprocal of rate) to fill the cistern.   From 9:00 AM to 10:00 AM, so in 1 hours, the inlet pipes will fill (time)*(rate) = 1*3/4 = 3/4 th of the cistern .   Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.   Letting x to be the rate of the outlet, we would have: 3/4 - x = 1/4 --&gt; x = 1/2 cistern/hour, which means that it takes 2 hours the outlet working alone to empty the cistern.   2 hoursnswer: 2 hours
<result>A</result>
There are two inlets and one outlet to a cistern. One of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:00AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?