$\frac{{{\theta _1} - {\theta _2}}}{t} = K\,\left[ {\frac{{{\theta _1} + {\theta _2}}}{2} - {\theta _0}} \right]$

For first process : $\frac{{(80 - 64)}}{5} = K\left[ {\frac{{80 + 64}}{2} - {\theta _0}} \right]$...$(i)$

For second process : $\frac{{(80 - 52)}}{{10}} = K\left[ {\frac{{80 + 52}}{2} - {\theta _0}} \right]$...$(ii)$

For third process : $\frac{{(80 - \theta )}}{{15}} = K\left[ {\frac{{80 + \theta }}{2} - {\theta _0}} \right]$…$(iii)$

On solving equation $(i)$ and $(ii)$ we get $K = \frac{1}{{15}}$ and ${\theta _0} = 24^\circ C$.

Putting these values in equation $(iii)$ we get $\theta = 42.7^\circ C$

$80\,^oC$ $\xrightarrow{5\,\,\min }64{{\,}^{o}}C$ ...... $(1)$

$80\,^oC$ $\xrightarrow{10\,\,\min }52{{\,}^{o}}C$...... $(2)$

$80\,^oC$ $\xrightarrow{15\,\,\min }\,\theta \,=$ ?...... $(3)$