As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2K$ are joined together to form a compound plate. The thickness of plates are $4.0 \mathrm{cm}$ and $2.5 \mathrm{cm}$ respectively and the area of cross-section is $120{ \mathrm{cm}}^2$ for each plate. The equivalent thermal conductivity of the compound plate is $\left(1+\frac{5}{\alpha }\right)K$, then the value of $\alpha$ will be _____ .