Question 127831: I need help with this math problem. Tarzan gave Jane a 1 pound box of chocolates. He knows that when they share a 1 pound box of chocolate it usually lasts for 2 weeks. When he eats a 1 pound box of chocolate, it lasts for 6 weeks. Based on this information, how long should it take Jane to eat a 1 pound box of chocolate by herself.
Any help would be appreciated! Thanks
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! When Tarzan eats a 1 lb box of chocolates, the box lasts for 6 weeks. Therefore, Tarzan's rate
of eating chocolate is 1/6 lb per week. This means that when he and Jane eat a box together in
two weeks, that he eats 1/6 box each week and in the two weeks he eats 2/6 of a box. And
2/6 reduces to 1/3. So in the two weeks that he and Jane polish off the chocolates, he
eats 1/3 of the box and Jane eats the other 2/3.
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Since Jane eats 2/3 of a box in 2 weeks, that means that each week she eats 1/3 of a box.
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From this you can tell that to eat a box by herself at 1/3 a box per week. It will take Jane
(a true choco-holic) 3 weeks to finish a box.
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That's the thought process to get the answer. To do it from the math process, you can
start by letting T represent Tarzan's rate of eating chocolate and J represent Jane's rate of
eating chocolate. When they work together they eat one (1) box of chocolates in 2 weeks.
The amount of chocolate each eats is determined by multiplying their rate of eating by the
time they eat, the time they eat being 2 weeks. In other words Tarzan eats T*2 and Jane
eats J*2 and this totals to 1 box. In equation form this is:
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T*2 + J*2 = 1
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But Tarzan's rate T comes from the fact that in 6 weeks at the rate he eats he finishes
one box. In equation form this is:
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T*6 = 1
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Solve for T by dividing both sides by 6 and you get:
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T = 1/6
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Substitute this value for T into the equation we wrote for Tarzan and Jane working
together and you convert:
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T*2 + J*2 = 1
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into:
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(1/6)*2 + J*2 = 1
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Multiply out the first term and you get:
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2/6 + J*2 = 1
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Get rid of the denominator by multiplying both sides (all terms on both sides) by 6. When you
do that multiplication of every term by 6 you get:
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2 + J*12 = 6
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Get rid of the 2 on the left side by subtracting 2 from both sides and you have:
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J*12 = 4
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Solve for J by dividing both sides by 12 to get:
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J = 4/12 = 1/3
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Now you can write the equation that says Jane's rate times W weeks equals 1 box of chocolate
by herself. In equation form this is:
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J*W = 1
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Substitute 1/3 for J and this equation becomes:
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(1/3)*W = 1
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Get rid of the denominator by multiplying both sides of this equation (all terms) by 3
and the result is:
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W = 3
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Jane eats a box of chocolates by herself in 3 weeks.
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Sometimes the math method of solving is confusing and if you really stop focusing on the
need to find an equation, you can think your way through the problem just as we did way
back at the beginning.
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Hope this helps you to understand the problem a little better.
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