Inequalities

Question

About 20% of the time you sleep is spent in a rapid eye movement (REM) sleep, which is associated with dreaming. If you sleep between 7 and 8 hours, how much is spent in REM sleep?

Answer 1

20% = 0.2

7 * .2 < x < 8 * .2

1.4 < x 1.6

Between 1.4 and 1.6 hours.

Answer 2

Let ρ represent REM time, which is one fifth of sleeping time t (overall).

 

7≤ t ≤8

 

Dividing by 5 (because 20% is one fifth) we get  7/5 ≤ t/5 ≤ 8/5

 

Now we convert to decimals and substitute  ρ for t/5:

 1.4 ≤ ρ ≤ 1.6