$13-20$ A compound reverted gear train is to be designed as a speed increaser to provide a total increase of speed of exactly $45$ to $1.$ With a $20$ pressure angle, specify appropriate numbers of teeth to minimize the gearbox size while avoiding the interference problem in the teeth. Assume all gears will have the same diametral pitch.

$13-22$ Repeat Problem $13-20$ for a gear ratio of exactly $30$ to $1.$

Please solve for $13-22$