In a 200 m race, runner A beats B by 35 m or by 7 seconds. What is the time taken by A to complete the 200 m course?

Introduction / Context:
This is a standard distance and time comparison question. We know that A finishes a 200 m race 35 m ahead of B and 7 seconds earlier. From the time difference and the distance B covers in that extra time, we can find B's speed, then B's total time, and finally A's time over the course. The problem checks comfort with speed = distance / time and basic algebra.

Given Data / Assumptions:
- Race distance is 200 m. - A beats B by 35 m. - A finishes 7 seconds before B. - All motion is at constant speed for each runner. - We must find A's time to cover 200 m.

Concept / Approach:
When A finishes 200 m, B has covered only 165 m. B needs to run the remaining 35 m in 7 seconds. That directly gives B's speed. With B's speed known, we can find how long B takes to run 200 m. Since A finishes 7 seconds earlier than B, subtracting 7 from B's time gives A's finishing time.

Step-by-Step Solution:
Step 1: At the moment A finishes 200 m, B has covered 200 - 35 = 165 m. Step 2: B still needs to run 35 m and takes 7 seconds more to finish. Step 3: Speed of B = distance / time = 35 / 7 = 5 m per second. Step 4: Time taken by B to run the full 200 m = 200 / 5 = 40 seconds. Step 5: A is 7 seconds faster, so time taken by A = 40 - 7 = 33 seconds.

Verification / Alternative check:
If A takes 33 seconds for 200 m, speed of A is 200 / 33 m per second. B takes 40 seconds, so B's speed is 5 m per second. In 33 seconds B runs 5 * 33 = 165 m, which is 35 m behind the finish line, and to run the extra 35 m at 5 m per second, B needs exactly 7 more seconds. This matches both the given distance gap and time gap, confirming that A's time is 33 seconds.

Why Other Options Are Wrong:
- 40 sec: This is B's time, not A's. - 47 sec: Larger than B's time and inconsistent with the statement that A finishes earlier. - None of these: Incorrect because 33 seconds is a consistent and valid answer.

Common Pitfalls:
Students sometimes apply the 7 second difference the wrong way round and add it to B's time instead of subtracting it to find A's time. Another common error is using 35 m divided by 7 seconds to get a speed but then mistakenly treating that speed as A's rather than B's. Carefully tracking which runner each piece of information refers to avoids these issues.

Final Answer:
A takes 33 seconds to complete the 200 m race.