A baby goes to sleep at 8 p. m., wakes up after two hours, stays awake for 15 minutes, and then goes back to sleep. If the baby repeats this sleep pattern until she is awakened at 6 a. m., what percent of the time from 8 p. m. to 6 a. m. was the baby asleep?

87.5%

Step-by-step explanation:

I am not sure how to set this up ... so I am just gonna try to figure this a different way ... without any formula

8 p. m - 10 pm ... awake for 15 minutes

10 pm - 12 am ... awake 15 minutes

12 am - 2 am ... awake 15 minutes

2 am to 4 am ... awake 15 minutes

4 am to 6 am ... awake 15 minutes

so from 8 pm to 6 am ... that is a total of 10 hrs ... and in those 10 hrs, the baby was awake 5 (15) = 75 minutes ... change 10 hrs to minutes ... 1 hr = 60 min ... so 10 hrs = (10 * 60) = 600 minutes

so in 600 minutes, the baby was awake 75 minutes ... that means the baby was asleep (600 - 75) = 525 minutes

525/600 = 0.875 = 87.5% <== = baby was asleep

or maybe this way ... for every 2 hrs, the baby was awake 15 minutes ... means the baby was asleep (120 - 15) = 105 minutes.

2 / 105 = 10 / x

2x = 1050

x = 1050/2

x = 525 minutes ... so the baby was asleep 525 minutes out of 600 minutes.

525/600 = 0.875 = 87.5%

I am getting the same answer either way

Step-by-step explanation:

If the baby repeats this sleep pattern until she is awakened at 6 a. m., what ... We have 10 hours between 8PM and 6AM = 10 * 60 = 600 minutes ... Awake 12:15 - 12:30 ... There are 4 periods of 2 hour sleep and 1 period of 1 hour sleep = 4*2 (60) + 1 (60) ... So 540/600 = 54/60 = 9/10 = 90% of the time asleep.