Question

Sumit can row a distance of 9 km in one hour in still water and he can now row the same distance in 45 minutes with the current. Find the total time taken by him to row 36 km with the current and return to the starting point.

• A. 8 hrs
• B. 9 hrs
• C. 10 hrs
• D. 12 hrs

Hint:

Use the relation: \[ \text{Speed with current} = b + c, \quad \text{Speed against current} = b - c \] where \( b \) is the speed in still water and \( c \) is the speed of the current.

Answer 1

The Correct Option is B

Step 1: Determine speeds in still water and with the current.
Speed in still water = \( \frac{9 \text{ km}}{1 \text{ hr}} = 9 \text{ km/hr} \)
Speed with the current = \( \frac{9 \text{ km}}{45/60 \text{ hr}} = \frac{9}{0.75} = 12 \text{ km/hr} \) Step 2: Find the speed of the current.
Let the speed of the current be \( c \). Then: \[ 9 + c = 12 \quad \Rightarrow \quad c = 3 \text{ km/hr} \] Step 3: Calculate upstream speed (against the current).
\[ \text{Upstream speed} = 9 - 3 = 6 \text{ km/hr} \] Step 4: Calculate time to row 36 km downstream and return 36 km upstream.
Downstream time = \( \frac{36}{12} = 3 \text{ hrs} \)
Upstream time = \( \frac{36}{6} = 6 \text{ hrs} \) Step 5: Total time taken:
\[ \text{Total time} = 3 + 6 = 9 \text{ hrs} \]