In a 20 m race, A runs at 2 m/s. A gives B a 10 m head-start and still beats B by 5 seconds. What is B’s speed (in m/s)?

Introduction / Context:
Head-starts alter distances while speeds remain constant. If one runner finishes earlier by a known time margin, we set up times for each runner and equate the difference to the given head-to-head gap in seconds.

Given Data / Assumptions:

• Total race distance from A’s mark = 20 m.
• A’s speed = 2 m/s ⇒ A’s time = 20 / 2 = 10 s.
• B starts 10 m ahead, so B needs to cover 10 m to finish.
• A beats B by 5 s ⇒ B’s time = 10 + 5 = 15 s.

Concept / Approach:
B’s average speed over their race distance equals distance / time. With B’s distance 10 m and time 15 s, compute vB. Ensure dimensions match.

Step-by-Step Solution:

Verification / Alternative check:
At 2/3 m/s, B covers 10 m in 15 s; A indeed finishes at 10 s, leading by 5 s, as stated.

Why Other Options Are Wrong:
1 m/s or 4/3 m/s would produce smaller/larger finish gaps than 5 s; 2 m/s is A’s speed, not B’s.

Common Pitfalls:
Using 20 m for B’s distance (ignoring the 10 m start) or mixing up “beats by 5 s” with “beats by 5 m”.

Final Answer:
2/3 m/s