Achild takes a nap averaging three hours and gets an average of 12 hours of sleep at night. nap time and night time sleep can each vary by 30 mins. what are the possible time lengths for the child's nap and night time sleep?

Since nap time averages 3 hrs, and can vary by 30 minutes (0.5 hrs), then nap time = 3 ± 0.25 hrs 

Since night time sleep averages 12 hrs, and can vary by 30 minutes (0.5 hrs), then night time sleep = 12 ± 0.25 hrs 

Minimum nap and night time sleep = 2.75 + 11.75 = 14.5 hrs 
Maximum nap and night time sleep = 3.25 + 12.25 = 15.5 hrs 
Nap and night time sleep = 15 ± 0.5 hrs 

Total sleep time averages 15 hrs and can vary by 1 hr (1/2 hr above or below 15 hrs)