Use the law of total probability:

$P(\text{melt}) = P(\text{rain}) \cdot P(\text{melt} \mid \text{rain}) + P(\text{no rain}) \cdot P(\text{melt} \mid \text{no rain})$

$= 0.5 \times 0.6 + 0.5 \times 0.1$

$= 0.30 + 0.05 = 0.35 = 35\%$