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

Question

1 month ago

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

e head start on Arnob. The graph shows how far they have both traveled.
How many minutes does it take Arnob to catch up to Kathleen?

a. 9.8
b. 10
c. 73.5
d. 75

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-03-01T09:37:19+03:00

<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.