SOLUTION: When Tristan visits Isolde on Valentine's Day, he's planning to bring her a one pound box of chocolates. He knows that when they share a one pound box of chocolates, it usually las

Algebra ->  Equations -> SOLUTION: When Tristan visits Isolde on Valentine's Day, he's planning to bring her a one pound box of chocolates. He knows that when they share a one pound box of chocolates, it usually las      Log On


   

Question 27313: When Tristan visits Isolde on Valentine's Day, he's planning to bring her a one pound box of chocolates. He knows that when they share a one pound box of chocolates, it usually lasts for two weeks. When he eats a one pound box of chocolates on his own it lasts for six weeks.
How long should a one pound box of chocolates last if Isolde eats it alone?
Remember to explain how you solved the problem and show how you know you are correct.
Note: Assume they don't eat faster or slower when they are alone.
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
For this problem, we set up two variables, "t" is the rate (in boxes/week) that Tristan eats and "s" is the rate (boxes/week) that Isolde eats. We know that rate (boxes/week) times time (weeks) gives the number of boxes eaten.
So if "they share a box it last for two weeks" means that they're both contributing their rates (s & t) for two weeks (2) and in that time eating one (1) box, or:
%28s%2Bt%29%282%29=1
The other equation says that "he eats a box of chocolates in 6 weeks" or:
t%2A6=1 which rearranges to:
t=1%2F6
Substituting into the first equation:
%28s%2B1%2F6%29%282%29=1
2s%2B1%2F3=1
2s=2%2F3
s=1%2F3
So she's her "eating rate" is 1/3 boxes/week, so she will finish a box of candy alone in 3 weeks.