In a 200 metre race, A beats B by 35 metres or 7 seconds. What is A's time to complete the 200 metre race?

Introduction / Context:
This question describes a race result both in terms of distance (35 metres) and time (7 seconds). A beats B by 35 metres or 7 seconds in a 200 metre race. This means that when A finishes, B is 35 metres behind and needs 7 more seconds to finish the race. From this, you can find B's speed and then use it to calculate A's time for the race. Understanding such equivalences is essential in races and games problems.

Given Data / Assumptions:

• Race distance = 200 m.
• A beats B by 35 m or 7 seconds.
• When A finishes 200 m, B has covered 200 - 35 = 165 m.
• B takes 7 seconds to cover the remaining 35 m.
• Speeds are constant for both runners.
• We must compute A's time to complete 200 m.

Concept / Approach:
Key steps:

• First find B's speed from the information about the last 35 m.
• Compute B's time to run the entire 200 m.
• The time A takes is equal to the time B needs to run 165 m, since at that instant A has finished 200 m and B is at 165 m.
• Using B's speed, find that time and hence A's race time.

Step-by-Step Solution:
Step 1: B covers 35 m in 7 seconds. Step 2: B's speed v_B = distance / time = 35 / 7 = 5 m/s. Step 3: B's time to cover the full 200 m = 200 / 5 = 40 seconds. Step 4: At the moment A finishes the race, B is only at 165 m (35 m behind). Step 5: Time taken by B to reach 165 m = distance / speed = 165 / 5 = 33 seconds. Step 6: Since both started together, A's time to run 200 m equals B's time to reach 165 m. Step 7: Therefore, A's race time is 33 seconds.

Verification / Alternative check:
Check with speeds:

• A's time = 33 s => A's speed v_A = 200 / 33 ≈ 6.06 m/s.
• B's speed v_B = 5 m/s.
• In 33 s, B covers distance = 5 * 33 = 165 m.
• Difference when A finishes = 200 - 165 = 35 m.
• B then takes additional time to cover 35 m = 35 / 5 = 7 seconds.

This matches the statement that A beats B by 35 m or 7 seconds, confirming that the computed time is correct.

Why Other Options Are Wrong:
40 sec is B's time, not A's, and gives no lead for A if misapplied.
47sec and "none of these" do not satisfy the condition of 35 m or 7 seconds gap. If you plug them into the speed equations, the resulting differences between A and B do not match the given race outcome.
Only 33sec yields the correct combination of distance and time advantage.

Common Pitfalls:
Many students misinterpret "35 metres or 7 seconds" and incorrectly think the two pieces of information are separate rather than equivalent descriptions of the same race outcome. Another common mistake is to assume that 7 seconds is the time difference between A and B's start, which is not true. It actually represents the additional time B needs to finish after A. Always translate the wording into precise positions and times before doing any calculations.

Final Answer:
Runner A completes the 200 metre race in 33 seconds.