Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mil

<span>To tackle the above dilemma,

we utilize the formula speed = distance/time.

Observing the red line:/>A covers 8 miles in 60 minutes, thus his speed reaches 8 miles per hour while K manages 2 miles in 30 minutes, resulting in her speed of 4 miles per hour, with a 5-mile head start.</span><span>A's distance = initial gate distance + (speed x time)
A's distance = 0 + (8 x time)

K's distance = initial gate distance + (speed x time)
K's distance = 5 + (4 x time)

For them to have traveled equal distances from the gate, they must have caught up with each other.
Therefore, when:

A's distance = K's distance
0 + (8 x time) = 5 + (4 x time)
8t = 5 + 4t
8t - 4t = 5
4t = 5
t = 5/4 hours
t = 1 hour and 15 minutes
t = 75 minutes
</span>
The solution is option D. I hope this clarifies the issue.

In this scenario, the first step is to assign variables.

We define:

x: time measured in minutes

y: distance covered.

The equations formulated are as follows:

For Kathleen:

For Arnob:

At the moment Arnob meets Kathleen, we have:

Next, we isolate x.

We now have:

Answer:

Arnob takes a total of 75 minutes to catch up to Kathleen:

d. 75