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1st question on this forum, and I know it will be an easy-peasy one for someone out there!! I'm not even sure if the title of the question is accurate for the question I am asking.....I'm also not sure what tags to put it under!

Anyway, here goes....

I have a line (l) which is of an arbitrary length, which represents an arbitrary range of minutes (r).

For example, the line is 900 wide and represents 720 minutes.

How do I work out, as a percentage of l, what one minute is?



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up vote 0 down vote accepted

Algebraic Mastmin is correct in that the percentage is independent of the length, and that each minute is $\frac{100}{720} = \frac{5}{36}$ percent of the line. But I thought you might also be interested in how long a minute is (in length) on the line.

If there are 720 minutes on the line, one minut is $\frac{1}{720}$ of this line. To get a better understanding of why this is correct, you can try adding them together again: $$ \underbrace{\frac{1}{720} + \frac{1}{720} + \cdots + \frac{1}{720}}_{\text{720 times}} = 720 \cdot \frac{1}{720} = \frac{720}{720} = 1$$ We see that we get the whole line. Now we need to find out the length of $\frac{1}{720}$ of that line. The length of the whole line is 900. We want $\frac{1}{720}$ of that. $$\frac{900}{720} = \frac{5}{4}$$ You can try for yourself to multiply this by 720 and see that you get the length of the line. We see that each minute is $\frac{5}{4}$ long.

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The percentage is independent of the length of the line segment. If there are 720 minutes in total, 1 minute is 1/720th of this, or 100/720%.

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