Geometry Homework - Indirect Proofs

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KaieraAi

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The text of the question is:

BUISNESS Over the course of three days, Marcus spent one and one-half hours on a teleconference for his marketing firm. Use indirect reasoning to show that, on at least one day, Markus spent at least one half-hour on a teleconference.

So, I guess I don't understand the question very well? I'm not sure if it's asking me to just show the indirect reasoning, (Which would be "Marcus didn't spend at least one half-hour on one day on a telelconference", right?) or if it wants me to show an indirect proof. I'm really bad at proofs, I get so confused!
 
In an indirect argument, you assume the negation of what you're trying to prove, and try to arrive at a contradiction.

In this example we assume that Markus spent less than one-half hour on each of the three days. Suppose he spent x, y and z hours on days 1, 2 and 3 respectively. Then he spent x+y+z<.5+.5+.5=1.5 hours over the three days which contradicts the original assumption.
 
The only thing I'm a little confused on, is, what if x, y, and z were all different values? In all, you know that he spent 1.5 hours, but is there any place in the question where it says that they were the same amounts each day? Ugh. I feel like the question wording is terrible... :?
 
There is nothing in my argument that says that x, y and z are the same. In fact, I'm using different letters because they are most likely different (although it's entirely possible that 2 of them or all three are the same). If they were the same I would just use x for all 3. The important thing is that they are all less than .5 so that their sum is less than 1.5.

For example, maybe x=.3, y=.42 and z=.49. Then x+y+z=.3+.42+.49= 1.21 which is less than 1.5.
 
KaieraAi said:
In all, you know that he spent 1.5 hours
Click to expand...

The fact that you say this leads me to believe that you're missing the point of an indirect argument. We are assuming the negation of this statement.
 
Oh. I think I get it now. No matter what, he'd HAVE to spend at least half an our, not that he did spend half an hour. I figured out my problem, I guess the wording threw me off. Thanks. :wink:
 
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