To determine how long it will take for a leaky faucet that wastes 1/2 gallon of water every day to waste 15 2/5 gallons, we first convert 15 2/5 gallons into an improper fraction.
15 2/5 can be converted as follows:
-
Multiply the whole number (15) by the denominator (5):
15 * 5 = 75 -
Add the numerator (2):
75 + 2 = 77 -
Thus, 15 2/5 gallons is equal to \( \frac{77}{5} \) gallons.
Now, we will set up the equation to find the number of days (d) it takes for 15 2/5 gallons to be wasted, given the faucet wastes 1/2 gallon per day:
\[ d \times \frac{1}{2} = \frac{77}{5} \]
To solve for \( d \), multiply both sides by 2 to get rid of the fraction on the left side:
\[ d = \frac{77}{5} \times 2 \]
This simplifies to:
\[ d = \frac{154}{5} \]
Now, we convert \( \frac{154}{5} \) into a mixed number:
- Divide 154 by 5:
\( 154 \div 5 = 30 \) remainder 4.
So, \( \frac{154}{5} = 30 \frac{4}{5} \).
Thus, it will take 30 2/5 days for the leaky faucet to waste 15 2/5 gallons of water.
Final answer is:
30 2/5 days.
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