SOLUTION: A typical college student spends 1/3 of her waking time in class, 1/5 of her waking time eating, 1/10 of her waking time working out, 3 hrs studying, and 2.5 hrs doing other things

Algebra ->  Human-and-algebraic-language -> SOLUTION: A typical college student spends 1/3 of her waking time in class, 1/5 of her waking time eating, 1/10 of her waking time working out, 3 hrs studying, and 2.5 hrs doing other things      Log On


   

Question 141010: A typical college student spends 1/3 of her waking time in class, 1/5 of her waking time eating, 1/10 of her waking time working out, 3 hrs studying, and 2.5 hrs doing other things. How many hours of sleep does she get?
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's compose a combined fraction of the three given, so that we know what fraction of her waking time we have to work with with the other two figures:
w=%281%2F3%29x%2B%281%2F5%29x%2B%281%2F10%29x=%2819%2F30%29x
That is to say, 19/30 of her time is spent between class, eating, and working out. This leaves 11/30 of her time between studying and doing other things.
So, let's compose an equality that says the remaining time must equal the remaining fraction of her waking time:
%2811%2F30%29x=5.5
x=15.
This means that she is awake 15 out of every 24 hours. Thus, she sleeps for 24-15=9 hours per 24 hours.

Check:
class: 5
eating: 3
working out: 1.5
studying: 3
other: 2.5
--------
waking total:15
+sleep:9
waking+sleep total:24.
If you have further difficulty, please send me an E-mail via my "me" page. Hope this helped.