In a $800 \text{ metre}$ race, $A$ defeated $B$ by $15 \text{ seconds}$. If $A$'s speed was $8 \text{ km/hr}$, the speed of $B$ was

### Concept & Simple Time-Distance When you know the distance and speed of one runner, you can find their total time. If they beat a second runner by a specific time, you add that time to find the second runner's total time. ### Step-by-Step Solution * **Convert A's speed:** $8 \text{ km/hr} = 8 \times \frac{5}{18} = \frac{20}{9} \text{ m/sec}$. * **Find A's time:** Time taken by $A$ to cover $800 \text{ m}$ is $\frac{800}{\frac{20}{9}} = 800 \times \frac{9}{20} = 360 \text{ seconds}$. * $A$ defeated $B$ by $15 \text{ seconds}$, meaning $B$ took $15 \text{ seconds}$ longer to finish. * **Find B's time:** Time taken by $B = 360 + 15 = 375 \text{ seconds}$. * **Find B's speed:** $B$ covers $800 \text{ m}$ in $375 \text{ seconds}$. * Speed of $B = \frac{800}{375} \text{ m/sec} = \frac{32}{15} \text{ m/sec}$. * **Convert B's speed back to km/hr:** $\frac{32}{15} \times \frac{18}{5} = \frac{32 \times 6}{25} = \frac{192}{25} \text{ km/hr}$. * Converting to a mixed fraction: $192 \div 25 = 7$ with a remainder of $17$. Thus, $7 \frac{17}{25} \text{ km/hr}$. ### Exam Strategy & Shortcut Instead of converting back and forth, find times in hours if preferred, or rely on quick cancellation. $360\text{s} = 6 \text{ mins}$. $B$ takes $6.25 \text{ mins} = \frac{6.25}{60} \text{ hours}$. Speed $= \frac{0.8}{\frac{6.25}{60}} = \frac{48}{6.25} = \frac{192}{25}$. ### Common Pitfall A common error is to subtract $15 \text{ seconds}$ from $A$'s time instead of adding it. Remember, the winner takes *less* time. ### Final Answer Therefore, the correct answer is **$7 \frac{17}{25} \text{ km/hr}$**.