In a 100 m race, A finishes in 36 s and B in 45 s. By how many metres does A beat B?

Given data

• A's time for 100 m = 36 s ⇒ speed_A = 100/36 m/s.
• B's time for 100 m = 45 s ⇒ speed_B = 100/45 m/s.

Concept/ApproachWhen A finishes (at 36 s), B has run distance = speed_B × 36. The lead = 100 − that distance.

Step-by-step calculationDistance by B in 36 s = (100/45) × 36 = 80 mLead of A = 100 − 80 = 20 m

Verification/AlternativeTime gap = 45 − 36 = 9 s; at 3.75 m/s (B's speed), 9 s corresponds to 33.75 m for B to finish; equivalently, he was 20 m behind when A finished.

Common pitfallsUsing average of times or subtracting speeds directly without aligning times.

Final Answer20 m