Problem of the Week - Algebra and Up - Dec. 6, 2020 to Dec. 12, 2020

Algebra and Up: 

Question: Puppies sleep an average of 12 hours each day. Kittens sleep an average of 20 hours each day. If a puppy is 4 weeks older than a newborn kitten, then how old will the kitten be when the kitten and the puppy have gotten the same amount of sleep in total? 

Answer:  42 days

Solution:  There are 28 days in 4 weeks, so the puppy has gotten 12 × 28 = 336 hours of sleep by the time the kitten is born. We want to know when the amount of sleep is equal. The kitten sleeps at a rate of 20 hours per day, and the puppy sleeps 12 per day with a 336-hour lead. We can set up the following equation and solve for d days:

20d = 12d + 336

d = 42

The kitten will be 42 days old.