There are two inlets and one outlet to a cistern. One of the inlets takes 4 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 8:30 AM with the cistern completely empty, and at 10:30AM, 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?  Pick one.
A) 2 hours B) 2.5 hours C) 3 hours D) 3.5 hours E) 8 hours
The combined inflow rate of the two inlets is 1/4 + 1/8 = 3/8 cistern/hour. Thus, working together, it takes 8/3 hours (time is reciprocal of rate) to fill the cistern.   From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) =2*3/8 = 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: 3/8 - x = 1/4 --&gt; x = 1/8 cistern/hour, which means that it takes 8 hours the outlet working alone to empty the cistern.   Answer: 8 hours.
<result>E</result>
There are two inlets and one outlet to a cistern. One of the inlets takes 4 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 8:30 AM with the cistern completely empty, and at 10:30AM, 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?