If a boat goes $7$ km upstream in $42$ minutes and the speed of the stream is $3$ kmph, then the speed of the boat in still water is :

### Concept & Formula The upstream speed is the speed of the boat against the flow of the river. It is calculated by dividing distance by time, and conceptually equals the boat's speed in still water minus the stream's speed. $$ U = B - S $$ Where $U$ is Upstream speed, $B$ is Boat speed in still water, and $S$ is Stream speed. ### Step-by-Step Solution * **Given:** Upstream distance = $7$ km, Upstream time = $42$ minutes, Stream speed ($S$) = $3$ kmph. * First, convert the time from minutes to hours: $42 \text{ minutes} = \frac{42}{60} \text{ hours} = 0.7 \text{ hours}$. * Calculate the upstream speed ($U$): $U = \frac{\text{Distance}}{\text{Time}} = \frac{7}{0.7} = 10 \text{ km/hr}$. * Use the formula $U = B - S$ to find the boat's speed ($B$): $10 = B - 3$ $B = 10 + 3 = 13 \text{ km/hr}$. ### Exam Strategy & Shortcut Calculate upstream speed immediately as a fraction to avoid decimals: $7 \times \left(\frac{60}{42}\right) = 10$. Then simply add the stream speed to get the boat speed: $10 + 3 = 13$. ### Common Pitfall Forgetting to convert minutes to hours before calculating speed, which leads to completely incorrect units and answers. ### Final Answer Therefore, the correct answer is **13 km/hr**.