To find out how long it will take for 15 2/5 gallons to be wasted by a leaky faucet that wastes 12 gallons per day, we first convert 15 2/5 gallons into an improper fraction or a decimal:
15 2/5 = \(15 + \frac{2}{5} = \frac{75}{5} + \frac{2}{5} = \frac{77}{5}\) gallons.
Next, we can calculate the number of days it will take to waste \(\frac{77}{5}\) gallons at a rate of 12 gallons per day:
\[ \text{Days} = \frac{\text{Total gallons}}{\text{Gallons per day}} = \frac{\frac{77}{5}}{12} \]
To divide by 12, we can multiply by the reciprocal:
\[ \text{Days} = \frac{77}{5} \times \frac{1}{12} = \frac{77}{60} \]
Now we convert \(\frac{77}{60}\) into a mixed number to find out how many full days and the remaining fraction it represents:
\(\frac{77}{60}\) can be divided as follows:
- 60 fits into 77 once (1 time), which leaves us with a remainder: \(77 - 60 = 17\).
Thus, we have:
\[ \frac{77}{60} = 1 \frac{17}{60} \]
So, it will take approximately 1 day and \(\frac{17}{60}\) of a day. In decimal form, \(\frac{17}{60}\) is approximately 0.283 days.
Therefore, it takes about 1.283 days (or roughly 1 day and 6 hours and 47 minutes) for 15 2/5 gallons to be wasted by the leaky faucet.