One pump can fill a reservoir in 60 hours. Another pump can fill the same reservoir in 80 hours. a third can empty the reservoir

Question

aniked [119]

2 years ago

15

One pump can fill a reservoir in 60 hours. Another pump can fill the same reservoir in 80 hours. a third can empty the reservoir

in 90 hours. If all three pumps are operating at the same time, how long will it take to fill the reservoir?

Mathematics

2 answers:

steposvetlana [31] · Answer 1 · 2022-03-25T17:40:30+03:00

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!