To determine how much more the river needs to rise to reach the major flood stage of 13 feet, let's start by calculating its current elevation after the two measurements given.
- Starting elevation: 9 feet.
- First rise: 1 and 1/12 feet.
- Convert 1 and 1/12 feet to an improper fraction:
- 1 = 12/12, so 1 and 1/12 = 12/12 + 1/12 = 13/12 feet.
- Convert 1 and 1/12 feet to an improper fraction:
- Second rise: 1 and 5/12 feet.
- Convert 1 and 5/12 feet to an improper fraction:
- 1 = 12/12, so 1 and 5/12 = 12/12 + 5/12 = 17/12 feet.
- Convert 1 and 5/12 feet to an improper fraction:
Now, we add these rises to the initial measurement:
- Initial elevation: 9 feet = 9/1 = 108/12 feet (converting to twelfths for easy addition).
- First rise: 13/12 feet.
- Second rise: 17/12 feet.
Now, let's sum these values:
\[ \text{Total elevation} = \frac{108}{12} + \frac{13}{12} + \frac{17}{12} = \frac{108 + 13 + 17}{12} = \frac{138}{12}. \]
Now we can simplify \( \frac{138}{12} \):
\[ \frac{138}{12} = 11.5 \text{ feet}. \]
Now, we compare this with the major flood stage of 13 feet:
\[ \text{Required rise} = 13 - 11.5 = 1.5 \text{ feet}. \]
Thus, the river needs to rise 1.5 feet more to reach the major flood stage of 13 feet.