To determine how far the caterpillar can crawl in 1 minute, we start by analyzing its speed.
The caterpillar crawls \( \frac{12}{14} \) inches in \( \frac{1}{4} \) of a minute. We first simplify \( \frac{12}{14} \):
\[ \frac{12 \div 2}{14 \div 2} = \frac{6}{7} \text{ inches} \]
So, the caterpillar crawls \( \frac{6}{7} \) inches in \( \frac{1}{4} \) of a minute.
To find out how far the caterpillar can crawl in 1 minute, we need to find the equivalent distance for 4 times that duration (since \( 1 \text{ minute} = 4 \times \frac{1}{4} \text{ minute} \)):
\[ \text{Distance in 1 minute} = 4 \times \frac{6}{7} = \frac{24}{7} \text{ inches} \]
Now, to convert \( \frac{24}{7} \) into a mixed number:
\[ \frac{24}{7} = 3 \frac{3}{7} \text{ inches} \]
Thus, the final answer is:
The caterpillar can crawl \( \frac{24}{7} \) inches or \( 3 \frac{3}{7} \) inches in one minute.