Answer: 55.384 hours or 55 minutes and 23 seconds.
Step-by-step explanation:
You know that the filling rate of first pump is:
[tex]\frac{1}{60}t[/tex]
The filling rate of second pump is:
[tex]\frac{1}{80}t[/tex]
Since the third pump can empty the reservoir in 90 hours, the rate is:
[tex]\frac{1}{90}t[/tex]
Where "t" is the time in hours that will take fill the reservoir if all the three pumps are operating at the same time.
Knowing this, you can set up the following equation:
[tex]\frac{1}{60}t+\frac{1}{80}t-\frac{1}{90}t=1[/tex]
Finally, you must solve for "t". You get:
[tex]\frac{1}{60}t+\frac{1}{80}t-\frac{1}{90}t=1\\\\\frac{13}{720}t=1\\\\t=(1)(\frac{720}{13})\\\\t=55.384[/tex]
(55.384 hours or 55 minutes and 23 seconds)
