For a steel alloy it has been determined that a carburizing heat treatment of $11\mathrm{.}6h$ duration will raise the carbon concentration to $0\mathrm{.}390wt\%$ at a point $1\mathrm{.}70mm$ from the surface. Estimate the time necessary to achieve the same concentration at a $5\mathrm{.}30mm$ position for an identical steel and at the same carburizing temperature.

$t=,h$