A tank can be filled by one pump in 50 minutes and by another in 60 minutes. A third pump can drain the tank in 75 minutes. If all 3 pumps work simultaneously, how long will it take to fill the tank? (Answer in hours)

let's label each pump A, B, and C, just for convenience. A fills the tank by 1/50 every minute, B fills the tank by 1/60 every minute, and C drains it by 1/75 every minute. Now we can put them all into one function: t(1/50 + 1/60 - 1/75) = 1, where t = our time in minutes and 1 = the tank being full.

next, we solve for t: t = 300/7 minutes, or approximately 42.86 minutes.

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