1. **State the problem:** Two joggers run around a 440-yard track. One completes a lap in 8 minutes, the other in 6 minutes. We want to find the time when both arrive together at the starting point if they start simultaneously and keep their pace. 2. **Understand the problem:** The joggers meet at the starting point after completing whole numbers of laps. This means we need the least common multiple (LCM) of their lap times. 3. **Formula and rules:** The time for both to meet is the LCM of their lap times: $$\text{LCM}(8,6)$$ 4. **Calculate the LCM:** - Prime factors of 8: $$2^3$$ - Prime factors of 6: $$2 \times 3$$ 5. **Find LCM by taking highest powers:** $$\text{LCM}(8,6) = 2^3 \times 3 = 8 \times 3 = 24$$ 6. **Interpretation:** Both joggers will arrive together at the starting point after 24 minutes. **Final answer:** 24 minutes (Option B)