$2\mathrm{.}7.$ A plate$-$bearing test using a $30-$inch diameter rigid plate was made on a subgrade as well as on $10$ inches of gravel base course. The unit load required to cause settlement of $0\mathrm{.}2$ inch was $10$ psi and $40,$ respectively. Determine the required thickness of base course to sustain a $50,000-$pound tire, $100$ psi pressure, and maintain a deflection of $0\mathrm{.}2$ inch.