A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes.
Last month the mail carrier delivered mail on the morning route $16$ times and on the afternoon route $12$ times, for a total distance traveled of $141$ miles.
This month the mail carrier delivered mail on the morning route $10$ times and on the afternoon route $15$ times, for a total distance traveled of $123.75$ miles.
What is the distance of the morning route in miles?