A motorboat in still water travels at a speed of $36$ km/hr. It goes $56$ km upstream in $1$ hour $45$ minutes. The time taken by it to cover the same distance down the stream will be

### Concept & Formula Time taken to travel a distance is defined by $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$. We must first find the stream speed to calculate the downstream speed. $$ U = B - S $$ $$ D = B + S $$ ### Step-by-Step Solution * **Given:** Boat speed ($B$) = $36$ km/hr, Upstream distance = $56$ km, Upstream time = $1$ hour $45$ minutes. * Convert upstream time to hours: $1 \text{ hour } 45 \text{ minutes} = 1 + \frac{45}{60} = 1 + \frac{3}{4} = \frac{7}{4} \text{ hours}$. * Calculate Upstream speed ($U$): $U = \frac{56}{\frac{7}{4}} = 56 \times \frac{4}{7} = 32 \text{ km/hr}$. * Find Stream speed ($S$): $U = B - S \implies 32 = 36 - S \implies S = 4 \text{ km/hr}$. * Calculate Downstream speed ($D$): $D = B + S = 36 + 4 = 40 \text{ km/hr}$. * Calculate Downstream time for the same distance ($56$ km): $\text{Time} = \frac{56}{40} = 1.4 \text{ hours}$. * Convert $1.4$ hours back to hours and minutes: $1 \text{ hour} + (0.4 \times 60) \text{ minutes} = 1 \text{ hour } 24 \text{ minutes}$. ### Exam Strategy & Shortcut Once upstream speed is found ($32$), note that $B$ is midway between $U$ and $D$. $D = B + (B - U) = 36 + (36 - 32) = 40$. Time $= \frac{56}{40} = \frac{7}{5}$ hours $= 1 \frac{2}{5}$ hours $= 1$ hr $24$ min. ### Common Pitfall Miscalculating fractional hours. $1.4$ hours is often mistakenly read as $1$ hour and $40$ minutes instead of $1$ hour and $24$ minutes. ### Final Answer Therefore, the correct answer is **1 hour 24 minutes**.