$A$ and $B$ can cover a $200 \text{ m}$ race in $22 \text{ seconds}$ and $25 \text{ seconds}$ respectively. When $A$ finished the race, then $B$ is at what distance from the finishing line?

### Concept & Margin of Victory If $A$ finishes before $B$, the distance $B$ is from the finish line is equal to the distance $B$ covers during the time difference between their finishes. ### Step-by-Step Solution * $A$ finishes the race in $22 \text{ seconds}$. * $B$ finishes the race in $25 \text{ seconds}$. * When $A$ crosses the finish line (at $t = 22 \text{ s}$), $B$ still has $(25 - 22) = 3 \text{ seconds}$ of running left to do to complete the $200 \text{ m}$. * First, find the speed of $B$: Speed = $\frac{Distance}{Time} = \frac{200 \text{ m}}{25 \text{ s}} = 8 \text{ m/sec}$. * Next, calculate the distance $B$ runs in those final $3 \text{ seconds}$. * Distance = $\text{Speed} \times \text{Time} = 8 \text{ m/sec} \times 3 \text{ s} = 24 \text{ m}$. * Therefore, when $A$ finished, $B$ was $24 \text{ m}$ from the finishing line. ### Exam Strategy & Shortcut Fractional logic: $B$ has $3 \text{ seconds}$ left out of his total $25 \text{ seconds}$. This means $B$ still needs to cover $\frac{3}{25}$ of the total race distance when $A$ finishes. $\frac{3}{25} \times 200 = 24 \text{ m}$. This skips calculating speed entirely! ### Common Pitfall Trying to calculate $A$'s speed, which is irrelevant. The question focuses solely on $B$'s position at the $22\text{-second}$ mark. ### Final Answer Therefore, the correct answer is **24 m**.