A runs 200 m in 35 s while B runs 200 m in 38 s. By what distance does A beat B in a 200 m race?

Introduction / Context:
When finish times over the same course are known, the distance lead at the winner's finish time equals the slower runner's distance covered by then. Compute that distance using the slower runner's speed and the winner's finishing time.

Given Data / Assumptions:

• A's 200 m time = 35 s ⇒ A finishes at t = 35 s.
• B's 200 m time = 38 s ⇒ B's speed = 200/38 m/s.

Concept / Approach:
At t = 35 s, B has covered d = speed_B * 35. The lead is 200 − d. Express the exact value as a simplified fraction.

Step-by-Step Solution:
speed_B = 200/38 = 100/19 m/s B's distance at 35 s = (100/19)*35 = 3500/19 m Lead = 200 − 3500/19 = (3800 − 3500)/19 = 300/19 m 300/19 m = 15 + 15/19 m = 15 15/19 m

Verification / Alternative check:
As a decimal, 300/19 ≈ 15.789 m, consistent with A being slightly faster over 200 m.

Why Other Options Are Wrong:
15 m and 152⁄3 m (≈ 15.667 m) are close but not exact; 154⁄19 m ≈ 8.105 m is far too small.

Common Pitfalls:
Using (38 − 35) seconds directly as meters; mixing up average vs instantaneous speeds; rounding too early and losing precision.

Final Answer:
1515⁄19 m