Question

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?

Answer 1

55.4 hours

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,

`a = (1)/(60) \\ b = (1)/(80) \\ c = - (1)/(90)`

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

Thus,

`t(a + b + c) = 1`

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.

`a + b + c = (1)/(60) + (1)/(80) - (1)/(90) \\ a + b + c = (13)/(720) \\ (720)/(13) (a + b + c) = 1`

Thus, t = 720/13 = 55.4 hours

Answer 2

55.384

Explanation: