one pump, let's call it A, fills the reservoir by 1/60 every hour. Now, B fills it by 1/80 every hour. C empties it by 1/90 every hour. All three are on, so now we combine them into one function: t(1/60 + 1/80 - 1/90) = 1, where t = the time it takes to fill it, and 1 is just our "reservoir finally filled" marker.
isolate t onto one side and we see t = 720/13 exactly, or approximately 55.38 hours. let me know if this is the wrong answer but I'm pretty sure it is correct!
Answer:
1/time needed = 1/time of 1st pump + 1/time of 2nd pump - 1/time of 3rd pump
1/t = 1/t1 + 1/t2 - 1/t3
1/t = 1/60 + 1/80 - 1/90
1/t = 12/720 + 9/720 - 8/720
1/t = 13/720
t = 720/13 hours = 55.38 hours = 55 hours 23 minutes
