The outer surface of a steel gear is to be hardened by increasing its carbon content; the carbon is to be supplied from an external carbon-rich atmosphere that is maintained at an elevated temperature. A diffusion heat treatment at 620?C for 103 min increases the carbon concentration to 0.75 wt% at a position 0.54 mm below the surface. Estimate the diffusion time (in min) required at 900?C to achieve this same concentration at a 0.54-mm position.