(p[1] - p[0]) / (40 * (c[0] - c[1])) < H price of the closer apartment minus price of the cheaper apartment divided by the the longer commute minus the shorter

(p[1] - p[0]) / (40 * (c[0] - c[1])) < H price of the closer apartment minus price of the cheaper apartment divided by the the longer commute minus the shorter commute (aggregated over a month). If that's greater than your hourly rate, then you're paying "more" to live closer ... if it's less, then you're saving money. (more or less, anyway)