Final answer:
The constant of variation (k) when 10 students can clean a 2 mile stretch in 1 hour is 1/10, meaning each student contributes to 1/10 of the work per hour. When only 8 students are available, the time required to clean the same stretch is 1.25 hours based on the work rate.
Step-by-step explanation:
Given that 10 students can clean up trash on a 2 mile stretch of road in 1 hour, we can establish a constant of variation to describe the work done. This constant (k) represents the work rate of the students and is calculated by the formula k = W / x, where W is the amount of work done, and x is the number of students. Since the work (cleaning 2 miles of road) remains constant, W is fixed. For 10 students working together, they accomplish 1 W in 1 hour, so k = 1/10.
When only 8 students are present, the time (t) it takes to clean the same stretch of road can be found by rearranging the formula to t = W / (k * x). Plugging the values in, we get t = 1 / (1/10 * 8), which simplifies to t = 1.25 hours. Therefore, it will take 8 students 1.25 hours to clean the 2 mile stretch of road.