A chemical reactor operates isothermally at a temperature of 300 K and is filled with a reaction mixture containing A, B and C. The reaction kinetics can be represented by the following reaction rate equation:

-d[A]/dt = k[A]^2[B]

Where [A], [B] and [C] are the molar concentrations of A, B, and C respectively, k is the reaction rate constant (0.01 mol^-2 dm^6/mol^2 s) and t is the time. The initial molar concentration of A in the reactor is 0.5 mol/dm^3 and the initial molar concentration of B is 0.1 mol/dm^3. The reaction continues until [A] = 0.1 mol/dm^3.

Determine the time required for [A] to decrease from 0.5 mol/dm^3 to 0.1 mol/dm^3.

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