Question

shay rides a bike at a constant speed. she rides 24 miles in 2 hours. what does the constant of proportionality of 12 mean?
hours miles
2 ×12 24
1 ×12 12
the constant of proportionality of 12 means that shay
bikes 12 miles every hour
bikes 1 mile every 12 hours

Explanation:

To determine the meaning of the constant of proportionality (12), we analyze the relationship between hours and miles. The formula for speed (which is the constant of proportionality here) is \( \text{speed} = \frac{\text{distance}}{\text{time}} \). For 2 hours and 24 miles, \( \frac{24}{2} = 12 \), and for 1 hour, \( 1\times12 = 12 \) miles. This shows that for each hour (time unit), the distance (miles) is 12. The option "bikes 1 mile every 12 hours" is incorrect because it would imply a very slow speed, inconsistent with the given data (24 miles in 2 hours is 12 miles per hour, not 1 mile in 12 hours).

Answer:

bikes 12 miles every hour