To find out how many bags of clothes John collected, we start by determining how many bags Matt collected.
Matt collected \( 7 \frac{1}{5} \) bags. We can convert this mixed number to an improper fraction:
\[ 7 \frac{1}{5} = 7 + \frac{1}{5} = \frac{35}{5} + \frac{1}{5} = \frac{36}{5} \]
Now that we know Matt collected \( \frac{36}{5} \) bags, we can find how many bags John collected. According to the problem, John collected \( \frac{1}{6} \) as many bags as Matt did. Therefore, we calculate:
\[ \text{John's bags} = \frac{1}{6} \times \frac{36}{5} = \frac{36}{30} \]
Now we can simplify \( \frac{36}{30} \):
\[ \frac{36}{30} = \frac{6}{5} \]
Next, we can convert \( \frac{6}{5} \) to a mixed number:
\[ \frac{6}{5} = 1 \frac{1}{5} \]
Thus, the number of bags of clothes that John collected is:
\[ \boxed{1 \frac{1}{5}} \text{ bags} \]
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