A child takes a nap avg 3 hrs & gets an avg of 12 hrs of sleep at night. Nap time & night time sleep can each vary by 30 mins. What're the possible time lengths for the child's nap & night time sleep?

Question

Hey, could I please get some help. I need the answer and an equation using an absolute value inequality. I know it may seem simple but I suck at making equations out of word problems.

Answer 1

Hi Nathan C.,

So, take the nap first: it can be 3 hrs. +/- 0.5 hrs., right? So arrange those extremes of nap time (least to greatest, in order) as the extremes of your inequality: 2.5 ≤ n ≤ 3.5 where times are in hrs., and n is nap time (it's appropriate to take the units outside when you're doing the actual math equations or inequalities. Just don't forget about them when you give the calculated answer!).

For the nighttime sleep, the limits are 12 hrs. +/- 0.5 hrs. I'll let you do the actual subtraction and addition on those limits, to get the same type of inequality as for nap time. Hint: use a different variable -- how about N?

Now for the real-world part: What are the limits on (nap + nighttime) sleep? As any parent of toddlers can tell you, when they nap too long, they're impossible to get to bed at night, so it's NOT 15 +/- 1 hrs. More like, variations in the nap time are canceled by opposite changes in the nighttime sleep. And the parent(s)' sleep time goes down too! Just sayin'.

-- Cheers, -- Mr. d.