A flat site is underlain by two layers over rock. The top layer is an SP with thickness $=2$m$.$ The second layer is a CL withthickness $=5$m$.$ A mid$-$layer sample of the CL reveals a recompression index of $0\mathrm{.}04,$ a compression index of $0\mathrm{.}3,$ a voidratio of $1\mathrm{.}2,$ a coefficient of consolidation of $0\mathrm{.}21$ m$/$day$,$ and a preconsolidation stress of $180$ kPa. The water table is located $1$m below the ground surface. A fill that imposes a load of $50$ kPa will be placed on the ground surface. Calculate the time $($in days$)$ it will take the CL layer to consolidate $50\%$ in response to placement of the fill. Assume that the soil above the water table is dry.