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?

55.4 hours

Step-by-step explanation:

Let A = First pump

B = Second pump

C = Third pump

From the given informations,

we know that A takes 60 hours to fill a reservoir.

Thus, it can be written as

% done by A in 60 hours = 100% = 1

60 (% done by A in 1 hour) = 1

% done by A in 1 hour = 1/60

Similarly,

% done by B in 1 hour = 1/80

% done by C in 1 hour =-(1/90)

Note: negative value because pump c is used to empty the reservoir.

Now we have formed three equations,

We want to find how long it takes to fill up the reservoir when three of them work together.

Thus,

where t is the time taken

a = % done by A in 1 hour

b = % done by B in 1 hour

c = % done by C in 1 hour

To find the value of t, just adds up the three equations formed previously.

Thus, t = 720/13 = 55.4 hours