One pump can fill a reservoir in 60 hours. another pump can fill the same reservoir in 80 hours. a third pump 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? pls solve and explain

approximately 5 hours 32 minutes

let x be the amount of it takes both pumps to fill and 1 pump to empty

so the pumps fill/empty at the rate of per hour

first pump fills at a rate of per hour

second pump fills at a rate of per hour

third pump empties at a rate of per hour

together the reservoir fills at a rate of

+ - =

multiply each term by 720x

120x + 90x - 80x = 720

130x = 720 ( divide both sides by 130 )

x = = 5. hours

(0. × 60 ≈ 32 minutes )

time taken to fill reservoir is 5 hours 32 minutes

468

step-by-step explanation: