Given the information in a$.)$ as well as the provided solution of $92$ mins for the pressure drop time of a$.),$ Solve b$.),$ please.

a$.)$ Furnace given in the figure has volume $0\mathrm{.}283$ m$3$ and contains air, which may be consider an ideal gas. The vacuum pump is pumping air out. During the pump out process, the heating coil in the tank hold temperature in the tank constant. The volumetric flow rate at the inlet of the pump, independent of pressure is $4\mathrm{.}7210-4$ m$3/$s$.$ How long does it take the pressure to fall from $1$ to $0\mathrm{.}0001$ atm? SA lake has surface area of $100$ km$2.$One river is bringing water into the lake at the rate of $1000$ m$3$s$,$while another is taking water out at $8000$ m$3$s$.$Evaporation and seepage are negligible.

b$.)$ Imagine that a tank has a leak that emits air at a rate of $7\mathrm{.}56*10^-7$ kg$/$s$.$ How long does it take the pump to reduce pressure from $1-0\mathrm{.}01$ atm?