Final answer:
The constant of proportionality (k) for Luisa running laps is 0.8 laps per minute. To convert laps to distance in meters on a standard 400-meter track, you divide the total desired distance by the length of one lap, resulting in 25 laps for 10 kilometers.
Step-by-step explanation:
To find the constant of proportionality (k) representing the number of laps Luisa can run per minute, simply divide the total number of laps by the total number of minutes. Given that Luisa can run 24 laps in 30 minutes, the calculation is k = 24/30, which simplifies to k = 0.8. Thus, Luisa can run 0.8 laps per minute.
To convert the number of track laps to a distance in meters, you must know the length of one lap on the track. For instance, if you are on a standard 400-meter track and you wish to cover 10 kilometers, you can use dimensional analysis. Calculate the number of laps by dividing 10 kilometers (10,000 meters) by the length of one lap (400 meters), which will give you 25 laps needed to cover the distance.