SOLUTION: 12. An aquarium can be filled by two inlets in 0.4 h and 0.25 h, respectively, and emptied by an outlet in 0.5 h. How long would it take to fill the aquarium if the inlets and ou

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Question 1191719: 12. An aquarium can be filled by two inlets in 0.4 h and 0.25 h,
respectively, and emptied by an outlet in 0.5 h. How long would it
take to fill the aquarium if the inlets and outlet were operating
simultaneously?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
12. An aquarium can be filled by two inlets in 0.4 h and 0.25 h,
respectively, and emptied by an outlet in 0.5 h. How long would it
take to fill the aquarium if the inlets and outlet were operating
simultaneously?
~~~~~~~~~~~~~~~~~~~~~ 

First  inlet filling rate is  1%2F0.4 = 2.5 volumes per hour.


Second inlet filling rate is  1%2F0.25 = 4 volumes per hour.


The total filling rate is  2.5 + 4 = 6.5 volumes per hour.


The draining rate is  1%2F0.5 = 2 volumes per hour.


The net filling rate (accounting for draining, too) is  6.5 - 2 = 4.5 volumes per hour.


The time for filling with all inlets and the outlet operating is  

    1%2F4.5 of an hour = 2%2F9  of an hour = %282%2A60%29%2F9 minutes = 40%2F3 minutes = 13 minutes and 20 seconds.    ANSWER

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor showed a standard solution using the rates of work of the two inlets and the outlet. Here is a very different approach to this kind of "working together" problem that many students like because it avoids having to solve equations with fractions.

The three times are 0.4, 0.25, and 0.5 hours; a common multiple of those times is 2 hours. So consider the work that could be done by the two inlets and the outlet in 2 hours.

The inlet that can fill the aquarium alone in 0.4 hours can fill it 2.0/0.4 = 5 times in 2 hours; the inlet that can fill it alone in 0.25 hours can fill it 2.0/0.25 = 8 times in 2 hours; and the outlet that can drain the tank in 0.5 hours can drain it 2.0/0.5 = 4 times in 2 hours.

So in 2 hours, the aquarium could be filled 5+8=13 times and drained 4 times, for a net of 9 times.

Therefore, the amount of time required to fill the aquarium if all the inlets and outlets are operating is 2/9 hours, or 120/9=40/3 minutes, or 13 1/3 minutes, or 13 minutes and 20 seconds.