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 : 30 am , 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 ?
"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 - - > x = 1 / 8 cistern / hour , which means that it takes 8 hours the outlet working alone to empty the cistern . answer : e ."
subtract(10, subtract(8, subtract(const_2.0, 1)))