Question

The National Sleep Foundation reported that teenagers need $9\frac{1}{4}$ hours of sleep every night to perform at their best during the day, and that it isn't natural for teenagers to be able to fall asleep before 11:00 at night. My alarm goes off at 6:20 a.m. on weekdays. Even if I fell asleep at exactly 11:00 on the school nights, how far under the $9\frac{1}{4}$ quota would I be? Give your answer in hours as a mixed number. (Assume that I am a teenager.)

Answer 1

Sleeping from 11:00 to 6:20 gets me

7+20/60=7 1/3 hours.

That leaves a sleep deficit of

9 1/4 - 7 1/3 = 9 3/12 - 7 4/12

(8+1) + 3/12-7 4/12=8 (12+3)/12 - 7 4/12

8 15/12 - 74/12 = 1 11/12 hours.

Note: This is also 1 hour and 55 minutes.