A sailor sails a distance of 48 km along the flow of a river in 8 h.If it takes 12 h to return the same distance,then the speed of the flow of the river is

Options

A. 0.5 km/h
B. 1 km/h
C. 1.5 km/h
D. 2 km/h

Answer

To solve the problem, we need to find the speed of the flow of the river based on the information provided about the sailor's journey. Let's break it down step by step.

### Step 1: Determine the speed of the sailor while going downstream.
The sailor travels 48 km downstream (with the flow of the river) in 8 hours.

**Formula:**
Speed = Distance / Time

**Calculation:**
Speed downstream (S + R) = 48 km / 8 h = 6 km/h

### Step 2: Determine the speed of the sailor while going upstream.
The sailor returns the same distance of 48 km upstream (against the flow of the river) in 12 hours.

**Formula:**
Speed = Distance / Time

**Calculation:**
Speed upstream (S - R) = 48 km / 12 h = 4 km/h

### Step 3: Set up the equations.
From the above calculations, we have two equations:
1. S + R = 6 (Equation 1)
2. S - R = 4 (Equation 2)

### Step 4: Solve the equations simultaneously.
To find the speed of the river (R), we can add both equations to eliminate S.

**Calculation:**
(S + R) + (S - R) = 6 + 4
2S = 10
S = 10 / 2 = 5 km/h

### Step 5: Substitute S back to find R.
Now, substitute S = 5 km/h into either Equation 1 or Equation 2. We'll use Equation 1.

**Calculation:**
5 + R = 6
R = 6 - 5
R = 1 km/h

### Conclusion:
The speed of the flow of the river is **1 km/h**.

---