1 km race lead with time info: In a 1 km race, P beats Q by 72 m in 12 s. Find P’s time for the whole course.

Introduction / Context:
We infer Q’s speed from the fact that 72 m corresponds to 12 s. Then we evaluate the shared finish time when P ends the race and compute P’s course time.

Given Data / Assumptions:

• Total = 1000 m
• Q is 72 m short when P finishes
• Q needs 12 s for 72 m ⇒ v_Q = 6 m/s

Concept / Approach:
At P’s finish, Q has covered 928 m at 6 m/s. That time equals P’s course time.

Step-by-Step Solution:

Verification / Alternative check:
Check that in an additional 12 s, Q would finish; 154 2/3 + 12 = 166 2/3 s for Q’s 1000 m, matching v_Q = 6 m/s (1000 / 166 2/3 = 6).

Why Other Options Are Wrong:
They do not align with v_Q = 6 m/s and the 72 m/12 s relationship.

Common Pitfalls:
Using 1000 m for Q in the shared time instead of 928 m.

Final Answer:
1542/3 s