The surface of a steel gear of $1022$ steel $(0\mathrm{.}22$ wt $\%$ C $)$ is to be gas$-$carburized at $927C.$ Calculate the time necessary to increase the carbon content to $0\mathrm{.}3wt\%$ at $0\mathrm{.}011$ in$.$ below the surface of the gear. Assume the carbon content of the surface to be $1\mathrm{.}20wt\%.$ in iron