a) The unit rate of Kate's sewing productivity can be found by dividing the number of dresses by the number of days:
Kate sews 100 dresses in 20 days.
The unit rate is 100 dresses / 20 days = 5 dresses per day.
b) The unit rate of Kim's running speed can be found by dividing the distance by the time:
Kim runs 5 km in 30 minutes.
The unit rate is 5 km / 0.5 hour = 10 km/hour.
Therefore, the unit rate for Kate's sewing productivity is 5 dresses per day, and the unit rate for Kim's running speed is 10 km/hour.