A man can row 5 km/h in still water .if the rate of the current is 1 km/h it takes 5/4 hours to row to a place and back.how far is the place?

Options

A. 2 km
B. 2.5 km
C. 3 km/h
D. 4 km

Answer

To solve the problem, we need to determine the distance to the place the man is rowing to and back. Let's break down the steps:

### Step 1: Understand the speeds
- Speed of the man in still water = 5 km/h
- Speed of the current = 1 km/h

### Step 2: Calculate effective speeds
- When rowing downstream (with the current), the effective speed = Speed in still water + Speed of current = 5 km/h + 1 km/h = 6 km/h.
- When rowing upstream (against the current), the effective speed = Speed in still water - Speed of current = 5 km/h - 1 km/h = 4 km/h.

### Step 3: Let the distance to the place be 'd' km
- Time taken to row downstream to the place = Distance / Speed = d / 6 hours.
- Time taken to row upstream back = Distance / Speed = d / 4 hours.

### Step 4: Total time for the round trip
- Total time for the round trip = Time downstream + Time upstream = (d / 6) + (d / 4).

### Step 5: Set up the equation
- We know from the problem that the total time taken for the round trip is 5/4 hours.
- Therefore, we can set up the equation:
\[ \frac{d}{6} + \frac{d}{4} = \frac{5}{4} \]

### Step 6: Find a common denominator
- The least common multiple of 6 and 4 is 12. We can rewrite the equation:
\[ \frac{2d}{12} + \frac{3d}{12} = \frac{5}{4} \]
\[ \frac{5d}{12} = \frac{5}{4} \]

### Step 7: Solve for 'd'
- To eliminate the fraction, we can cross-multiply:
\[ 5d \cdot 4 = 5 \cdot 12 \]
\[ 20d = 60 \]
\[ d = \frac{60}{20} = 3 \]

### Step 8: Conclusion
- The distance to the place is **3 km**.

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