To find the unit rate of water dripped per day, we start with the information given:
The faucet drips \( \frac{2}{3} \) gallon of water in 10 hours.
First, we need to find out how many gallons drip in one hour. We can do this by dividing the total gallons by the total time in hours:
\[ \text{Rate per hour} = \frac{\frac{2}{3} \text{ gallon}}{10 \text{ hours}} = \frac{2}{3} \div 10 = \frac{2}{3} \times \frac{1}{10} = \frac{2}{30} = \frac{1}{15} \text{ gallon per hour} \]
Next, we want to convert the rate from per hour to per day. There are 24 hours in a day, so we multiply the rate per hour by 24:
\[ \text{Rate per day} = \frac{1}{15} \text{ gallon per hour} \times 24 \text{ hours} = \frac{24}{15} \text{ gallons} \]
Now, simplify \( \frac{24}{15} \):
\[ \frac{24}{15} = \frac{8}{5} = 1 \frac{3}{5} \text{ gallons per day} \]
Thus, the unit rate of water dripped per day is:
C: \( 1 \frac{3}{5} \) gallons per day.
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