Answer:
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,
[tex]a = \frac{1}{60} \\ b = \frac{1}{80} \\ c = - \frac{1}{90} [/tex]
We want to find how long it takes to fill up the reservoir when three of them work together.
Thus,
[tex]t(a + b + c) = 1[/tex]
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.
[tex]a + b + c = \frac{1}{60} + \frac{1}{80} - \frac{1}{90} \\ a + b + c = \frac{13}{720} \\ \frac{720}{13} (a + b + c) = 1[/tex]
Thus, t = 720/13 = 55.4 hours
