$(15\%)10.$ A concrete mixture has been designed for the construction of concrete pavements in $$mir$.$ The mixture design parameters are; $\frac{w}{c}=0\mathrm{.}50,$ CEM I $42\mathrm{.}5$R cement, and no air entrainment. Cylinders were prepared from the mixture, cured at $20C$ in the laboratory and tested in compression at $1,7,28,$ and $90$ days of age. Using this data, the compressive strength of the concrete has been plotted vs$.$ time.

$($a$)$ A tensile strength of $3$MPa is required before the concrete can be opened to traffic loading. Estimate at what age the concrete you designed will reach that strength. $($assume that tensile strength is $\frac{1}{10}$ of its compressive strength$)$

$($b$)$ The average temperature during concreting and curing is measured as $8C$ on site. Estimate when site concrete reaches the $28-$day strength of laboratory concrete. Maturity $=a_t(T+10)$