Question 1191719
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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.<br>
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.<br>
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.<br>
So in 2 hours, the aquarium could be filled 5+8=13 times and drained 4 times, for a net of 9 times.<br>
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.<br>