Every day Drake runs two laps at a park in his neighborhood. His speed, s, is inversely proportional to time, t, over the same distance. If Drake runs at a speed of 6 miles/hour, it takes him half an hour to complete two laps of the park. Which statement best describes Drake’s situation?

statements?

2 miles

Joe

To solve this problem, we need to understand the relationship between speed and time. The question states that Drake's speed, s, is inversely proportional to time, t. This means that as time increases, his speed decreases, and as time decreases, his speed increases.

Let's assign variables to the given information:
- Drake's speed, s = 6 miles/hour
- Time, t = 0.5 hours (since he completes two laps in half an hour)

We can use the formula for inverse proportionality: s = k/t, where k is the constant of proportionality.

To find the value of k, we can plug in the given values:
6 = k/0.5

To solve for k, we can multiply both sides of the equation by 0.5:
6 * 0.5 = k

The value of k is 3.

Now that we have the value of k, we can write the equation for the relationship between speed and time: s = 3/t.

Next, let's test this equation with different values of t:
- When t = 0.5 hours (as given in the problem), s = 3/(0.5) = 6 miles/hour.
- When t = 1 hour, s = 3/(1) = 3 miles/hour.
- When t = 2 hours, s = 3/(2) = 1.5 miles/hour.

Based on these calculations, we can conclude that Drake's speed decreases as time increases, which aligns with the given statement that his speed is inversely proportional to time.

Therefore, the best statement to describe Drake's situation is that his speed is inversely proportional to the time taken to complete the two laps at the park.