To find out how many bins of bottles Lena collected, we first need to determine how many bins Ryan collected.
Ryan collected \( \frac{3}{5} \) of a bin.
Lena collected 42 times as many bins as Ryan: \[ \text{Lena's bins} = 42 \times \left( \frac{3}{5} \right) \]
Now we can perform the multiplication: \[ 42 \times \frac{3}{5} = \frac{42 \times 3}{5} = \frac{126}{5} \]
Now, let's convert \( \frac{126}{5} \) into a mixed number: \[ 126 \div 5 = 25 \quad \text{remainder } 1 \]
This can be expressed as: \[ 25 \text{ whole bins and } \frac{1}{5} \text{ of a bin} \]
Thus, expressing it as a mixed number, we have: \[ 25 \frac{1}{5} \]
So, Lena collected \( \frac{126}{5} \) bins or \( 25 \frac{1}{5} \) bins.
In conclusion, Lena collected: \[ \boxed{25 \frac{1}{5}} \] bins of bottles.