Diana and Rahima start running on a circular track at the same time. Diana completes one round in 48 minutes, and Rahima completes one round in 36 minutes. If they both start at 8:06 a.m. from the sta

This will be the time after which they meet again at the starting point.
Diana's time $= 48 \text{ minutes}$
Rahima's time $= 36 \text{ minutes}$

Prime factorization of 48:

$$48 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2^4 \times 3^1$$

Prime factorization of 36:

$$36 = 2 \times 18 = 2 \times 2 \times 9 = 2^2 \times 3^2$$

$$144 \text{ minutes} = \frac{144}{60} \text{ hours} = 2 \text{ hours and } 24 \text{ minutes}$$

(Since $2 \times 60 = 120$, and $144 - 120 = 24$)

Starting time $= 8:06 \text{ a.m.}$
Time to meet again $= 2 \text{ hours } 24 \text{ minutes}$
Meeting time $= 8:06 \text{ a.m.} + 2 \text{ hours } 24 \text{ minutes} = 10:30 \text{ a.m.}$

They will meet again at the starting point at 10:30 a.m.