A man can swim 5 km/h in still water. If the speed of current be 3 km/h, the time taken by him to swim to a place 16 km upstream and back is :

Options

A. 8 h
B. 7.5 h
C. 6.66 h
D. 10 h

Answer

To solve the problem step by step, we need to calculate the time taken by the man to swim 16 km upstream and then return back downstream.

### Step 1: Determine the swimming speeds
- The speed of the man in still water (x) = 5 km/h
- The speed of the current (y) = 3 km/h

### Step 2: Calculate the effective speeds
- **Upstream speed** = Speed in still water - Speed of current = x - y = 5 km/h - 3 km/h = 2 km/h
- **Downstream speed** = Speed in still water + Speed of current = x + y = 5 km/h + 3 km/h = 8 km/h

### Step 3: Calculate the time taken to swim upstream
- Distance upstream = 16 km
- Time taken to swim upstream = Distance / Speed = 16 km / 2 km/h = 8 hours

### Step 4: Calculate the time taken to swim downstream
- Distance downstream = 16 km
- Time taken to swim downstream = Distance / Speed = 16 km / 8 km/h = 2 hours

### Step 5: Calculate the total time taken for the round trip
- Total time = Time upstream + Time downstream = 8 hours + 2 hours = 10 hours

### Final Answer
The total time taken by the man to swim to the place 16 km upstream and back is **10 hours**.

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