The speed of a boat in still water is $15$ km/hr and the rate of current is $3$ km/hr. The distance travelled downstream in $12$ minutes is :

### Concept & Formula Distance is calculated as the product of speed and time. For a downstream journey, you must add the speed of the current to the speed of the boat in still water. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ $$ D = B + S $$ ### Step-by-Step Solution * **Given:** Boat speed ($B$) = $15$ km/hr, Stream speed ($S$) = $3$ km/hr, Time = $12$ minutes. * Calculate the downstream speed ($D$): $D = 15 + 3 = 18 \text{ km/hr}$. * Convert the given time from minutes into hours to match the speed units: $\text{Time} = \frac{12}{60} \text{ hours} = \frac{1}{5} \text{ hours}$. * Calculate the distance travelled: $\text{Distance} = 18 \times \left(\frac{1}{5}\right) = 3.6 \text{ km}$. ### Exam Strategy & Shortcut Think in terms of proportions: $12$ minutes is exactly $\frac{1}{5}$th of an hour. The downstream speed is $18$ km/hr, so the distance is simply $\frac{18}{5} = 3.6$ km. ### Common Pitfall Multiplying the speed by the time in minutes ($18 \times 12$) without converting the time to hours, resulting in massive overestimations. ### Final Answer Therefore, the correct answer is **3.6 km**.