The speed of the boat in still water is $5$ times that of the current, it takes $1.1$ hours to row to point B form point A downstream. The distance between point A and point B is $13.2$km. How much distance (in km) will it cover in $312$ minutes upstream? [IBPS—Bank Spl. Officer (IT) Exam, 2015]

### Concept & Relative Speeds Establish a ratio between the boat's speed and the current's speed to express downstream and upstream velocities in terms of a single variable. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution * Establish variables: Let current speed = $c$. The boat's still water speed is $5c$. * Determine relative speeds: Downstream Speed ($D$) = $5c + c = 6c$. Upstream Speed ($U$) = $5c - c = 4c$. * Find the actual value of $c$: The boat covers $13.2$ km in $1.1$ hours downstream. $D = \frac{13.2}{1.1} = 12$ km/h. Since $6c = 12$, we find $c = 2$ km/h. * Calculate Upstream Speed ($U$): $U = 4c = 4 \times 2 = 8$ km/h. * Calculate target distance: Time is $312$ minutes. Convert to hours: $\frac{312}{60} = 5.2$ hours. Distance = $U \times \text{Time} = 8 \times 5.2 = 41.6$ km. ### Exam Strategy & Shortcut The speed ratio of Downstream ($6c$) to Upstream ($4c$) is $6:4$ or $3:2$. If downstream speed is $12$ km/h, upstream speed is instantly $\frac{2}{3} \times 12 = 8$ km/h. Multiply by the hour equivalent of $312$ mins ($5.2$) to get $41.6$. ### Common Pitfall Forgetting to convert minutes to hours before multiplying with the calculated upstream speed in km/h. ### Final Answer Therefore, the correct answer is **(c) 41.6**.