In a 300 m race, runner A beats B by 22.5 m or by 6 seconds. What is the total time taken by B to complete the 300 m course?

Introduction / Context:
This question combines a distance lead and a time lead to find the actual speed and total time for one runner. It is a typical aptitude question that links distance, speed, and time in a race where one runner finishes earlier and also covers a longer distance. Understanding how to convert the given 22.5 m and 6 seconds into the speed of the slower runner is the key.

Given Data / Assumptions:
- Race length is 300 m. - A beats B by 22.5 m. - A also beats B by 6 seconds. - Speeds of both runners are constant over the entire race. - We must find B's time to run the whole 300 m.

Concept / Approach:
At the moment when A finishes the race, B is still 22.5 m behind the finish line. The 6 second time difference tells us that B needs 6 more seconds to run those remaining 22.5 m. This directly gives B's speed as distance divided by time. Once we know B's speed, we can compute the time B takes to cover the full 300 m. We do not need A's speed explicitly.

Step-by-Step Solution:
Step 1: When A finishes 300 m, B has covered 300 - 22.5 = 277.5 m. Step 2: B still needs to run 22.5 m to finish. Step 3: The time B takes to run these 22.5 m is given as 6 seconds. Step 4: Therefore speed of B = distance / time = 22.5 / 6 m per second. Step 5: Simplify that value: 22.5 / 6 = 3.75 m per second. Step 6: Now time taken by B to run the total 300 m = 300 / 3.75 seconds. Step 7: Calculate this quotient: 300 / 3.75 = 80 seconds.

Verification / Alternative check:
If B runs at 3.75 m per second, then in 80 seconds B covers 3.75 * 80 = 300 m, which matches the race length. In 74 seconds B would cover 277.5 m, leaving 22.5 m to be run in the remaining 6 seconds. Thus, B is exactly 22.5 m behind after A finishes, and the time gap of 6 seconds is maintained, so the numbers are internally consistent.

Why Other Options Are Wrong:
- 86 sec and 76 sec: These times do not yield both a 22.5 m distance gap and a 6 second time gap when combined with any consistent speed. - None of these: This would be correct only if no option matched the consistent calculation, but 80 seconds clearly does.

Common Pitfalls:
Students sometimes assume that the 6 second difference is the total time of B to run 22.5 m plus some unknown time, and they overcomplicate the equation. Others try to derive both speeds first, which is not necessary. The clean approach is to use the final 22.5 m and 6 seconds directly to find B's speed, and then scale that speed up to the full 300 m distance.

Final Answer:
B takes 80 seconds to complete the 300 m race.