[tone999]

A steel is hardened using a high temperature carburising process.
The evolution of the carbon concentration with depth d and time t
is given by the erf function:

cs-cd/cs-co = erf ( d/2 SQRT Dt)

Where, C, Cd and C, respectively represent the concentrations
of the diffusing species at the surface, deep d after time t and in
the bulk. The erf function has the following values:

x         erfx
0.3     0.329
0.35    0.379
0.4      0.428
0.45    0.475
0.5      0.520

Consider an initial carbon concentration of 0.15 wt%, if the surface
concentration is suddenly brought to 0.9 wt%, how long will it take
to achieve a 0.6 wt% at a position d=0.2 mm inside the metal?
(Assume a diffusion coefficient of carbon into steel of
2x10^-7 cm^2/s).