A smart water tank system has two automated pipes. Pipe U1 fills the tank in 5 hours and pipe V1 can drain the tank in 10 hours. Pipe U1 is operated alone for 2 hours, after which V1 is also activated. How much of the tank will be filled after total 5 hours?
\(\frac{7}{10}\)
Pipe U1 fills \(\frac{1}{5}\) of the tank per hour and pipe V1 drains \(\frac{1}{10}\) of the tank per hour.
In the first 2 hours only U1 works: filled part = \(2 \times \frac{1}{5} = \frac{2}{5}\).
For the remaining 5 – 2 = 3 hours both work, with net rate \(\frac{1}{5} - \frac{1}{10} = \frac{1}{10}\) per hour, so they add \(3 \times \frac{1}{10} = \frac{3}{10}\).
Total filled after 5 hours = \(\frac{2}{5} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}\).
Check: U1 runs all 5 hours and fills \(\frac{5}{5} = 1\) tank, V1 runs 3 hours and drains \(\frac{3}{10}\); \(1 - \frac{3}{10} = \frac{7}{10}\), the same result.
Hence, \(\frac{7}{10}\).
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