A man can row a distance of 6 km in 1 hour in still water. He can row the same distance in 45 minutes with the current. Find the total time taken by him to row a distance of 16 km with the current and to return to the starting point.

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Accepted Answer

Step 1: Calculate the speed in still water.
- Distance = 6 km, Time = 1 hour
- Speed in still water (S) = Distance / Time = 6 km/h

Step 2: Calculate the speed with the current.
- Distance = 6 km, Time = 45 minutes = 0.75 hours
- Speed with current (S + C) = 6 / 0.75 = 8 km/h

Step 3: Calculate the speed of the current (C).
- Since S = 6 km/h and S + C = 8 km/h
- C = 8 - 6 = 2 km/h

Step 4: Calculate the speed against the current (return speed).
- Speed against current (S - C) = 6 - 2 = 4 km/h

Step 5: Calculate the time taken to row 16 km with the current.
- Time with current = Distance / Speed with current = 16 / 8 = 2 hours

Step 6: Calculate the time taken to return 16 km against the current.
- Time against current = Distance / Speed against current = 16 / 4 = 4 hours

Step 7: Calculate total time.
- Total time = 2 hours + 4 hours = 6 hours

Step 8: Check options.
- Option 2 states 6 hours, but the question asks for total time taken to row 16 km with current and return.

Re-examining the question, it states "to row a distance of 16 km with the current and to return to the starting point." So total distance is 16 km downstream + 16 km upstream.

Total time = 2 hours (downstream) + 4 hours (upstream) = 6 hours.

Therefore, the correct answer is 6 hours.

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