It takes drew 1/10 hour to walk a 1/6 mile park loop. what is drew's unit rate, in miles per hour?

1/10 hour = 10 minutes

1/6 mile loop in 10 minutes.
1/6*6/1, 10*6=60
1 Mile every 60 minutes.

By unit rate, do you mean miles per hour? If so:
Drew walks 1 mile per hour.