Question

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)

Answer 1

To fill the tank when all three pumps are working simultaneously, it will take approximately 0.606 hours.

Step-by-step explanation:

To find the time it takes to fill the tank when all three pumps work simultaneously, we need to calculate their combined rate of filling the tank. The rate at which the first pump fills the tank is 1 tank/50 minutes = 1/50 tank per minute. Similarly, the second pump fills the tank at a rate of 1/60 tank per minute, and the third pump drains the tank at a rate of 1/75 tank per minute. Therefore, the combined rate of filling the tank is (1/50 + 1/60 - 1/75) tank per minute. To find the time it takes to fill the tank, we can take the reciprocal of the combined rate. Thus, it will take approximately 36.36 minutes to fill the tank, which is approximately 0.606 hours.

Answer 2

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.