Sam blinks 31,015 times during the 16 hours he is awake.
Assuming he sleeps for 8 hours, he will spend those with his eyes closed and not be blinking at all.
1. As there are 24 hours in a day, 24 - 8 = 16. Sam is awake for 16 hours of the day.
2. There are 60 minutes in an hour, and 60 seconds in a minute. So there are 3,600 seconds in an hour. 16 x 3,600 = 57,600. There are 57,600 seconds in 16 hours.
3. He blinks at a rate of 14 blinks per 26 seconds. Multiply the fraction 14/26 by 57,600 seconds. 14/26 also simplifies to 7/13. So, (7/13)*57,600 = 403,200/13
As a decimal, this is 31015.38461… or ≈ 31,015.4 blinks.
Sam blinks 31,015.4 times during the 16 hours he is awake. Since 0.4 of a blink is not a whole blink, I think it’s best to round to the nearest whole: 31,015.