To find the constant of proportionality based on Ruth's reading progress, we need to express her reading rate in relation to time.
Ruth reads 15 pages in 30 minutes. To find her rate per minute, we can set up the ratio:
\[ \text{Rate} = \frac{\text{Pages}}{\text{Time}} = \frac{15 \text{ pages}}{30 \text{ minutes}} = \frac{1}{2} \text{ pages/minute} \]
This means that for every minute, she reads \( \frac{1}{2} \) page.
Now, the options provided describe specific points that reflect ratios of pages to time or the time equivalent of a certain number of pages:
- \( (112, 30) \)
- \( \left( 1, \frac{1}{2} \right) \) - This one indicates she reads 1 page in 2 minutes.
- \( (15, 12) \)
- \( (2, 60) \) - This indicates reading 2 pages in 60 minutes.
To find the correct representation of her reading rate, we see that she can also read:
- 1 page in 2 minutes (which corresponds with \( \left( 1, \frac{1}{2} \right) \)).
This does not directly appear in the options, but the ratio \( \left( \frac{1}{2}, 30 \right) \) is equivalent to \( (1, 2) \), which matches the first option we calculated. The closest interpretation under the proper contexts could be \( \left( 1, \frac{1}{2} \right) \).
However, if we evaluate all options, the valid point showing the relation to time (where the reading rate is consistent with those provided) would match best with:
(1, 30) which would indicate 1 page would take 30 minutes if we simplified the ratio incorrectly.
Therefore, the answer options suggest a misunderstanding of the format, but examining strictly by the proportional information indicates (1, 30) could also align with points of everyday reading habits.
Conclusively, the ratio of pages read per minute provides a valid constant proportionality interpreted through:
\( (1, 30) \) as structural reflectivity, giving hints towards her rate which could assume additional interpretations of reading pace from gathered data.
1 answer