x : 3 1/5=4 5/6 : 3 13/15

To solve the equation \( x : 3 \frac{1}{5} = 4 \frac{5}{6} : 3 \frac{13}{15} \), we can rewrite the mixed numbers as improper fractions.

1. Convert the mixed numbers to improper fractions:

   • For \( 3 \frac{1}{5} \): \[ 3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5} \]

   • For \( 4 \frac{5}{6} \): \[ 4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6} \]

   • For \( 3 \frac{13}{15} \): \[ 3 \frac{13}{15} = \frac{3 \times 15 + 13}{15} = \frac{45 + 13}{15} = \frac{58}{15} \]

2. Substitute the improper fractions into the equation: \[ x : \frac{16}{5} = \frac{29}{6} : \frac{58}{15} \]

3. Calculate the right side \( \frac{29}{6} : \frac{58}{15} \): \[ \frac{29}{6} \div \frac{58}{15} = \frac{29}{6} \times \frac{15}{58} \]

   Notice that \( 58 = 2 \times 29 \), so we have: \[ \frac{29}{6} \times \frac{15}{2 \times 29} = \frac{15}{6 \times 2} = \frac{15}{12} = \frac{5}{4} \]

4. Now we have: \[ x : \frac{16}{5} = \frac{5}{4} \]

5. To find \( x \), we solve for it: \[ x = \frac{5}{4} \times \frac{16}{5} \]

6. The 5's cancel out: \[ x = \frac{16}{4} = 4 \]

Thus, the solution is: \[ \boxed{4} \]