Final answer:
Jonathan can jog 8 km in 64 minutes at the same rate he jogs 5 km in 40 minutes, using the concept of proportions to calculate the distance.
Step-by-step explanation:
Jonathan can jog 5 km in 40 minutes. If we want to find out how far he can jog in 64 minutes at the same rate, we need to use the concept of proportions to solve this problem. First, we'll set up a proportion where the distances are directly proportional to the times. Since we know the distance for a known time, we can find the distance for the new time.
We have the equation (5 km / 40 min) = (x km / 64 min), where x represents the distance Jonathan can jog in 64 minutes. By cross-multiplying and solving for x, we get x = (5 km × 64 min) / 40 min, which simplifies to x = (5 × 64) / 40. This simplifies further to x = 320 / 40, resulting in x = 8 km. Thus, Jonathan can jog 8 km in 64 minutes at the same rate.
Understanding how to solve these types of problems is essential in mathematics, especially when studying ratios and proportions, which are a key part of the middle school math curriculum.