A person rows a kilometre down the stream in 10 minutes and upstream in 30 minutes. Find the velocity of the stream -----

Options

A. 1 km/hr
B. 2 km/hr
C. 3 km/hr
D. 4 km/hr

Answer

To solve the problem step by step, we will use the information provided about the person's rowing times downstream and upstream to find the velocity of the stream.

### Step 1: Understand the Problem
A person rows 1 km downstream in 10 minutes and upstream in 30 minutes. We need to find the velocity of the stream.

### Step 2: Convert Time to Hours
Since the speeds are typically expressed in km/h, we need to convert the time from minutes to hours.
- Downstream time = 10 minutes = 10/60 hours = 1/6 hours
- Upstream time = 30 minutes = 30/60 hours = 1/2 hours

### Step 3: Calculate Speeds
Next, we calculate the downstream and upstream speeds.
- Downstream speed (v) = Distance / Time = 1 km / (1/6) hours = 6 km/h
- Upstream speed (u) = Distance / Time = 1 km / (1/2) hours = 2 km/h

### Step 4: Set Up Equations
Let:
- x = speed of the person in still water (km/h)
- y = speed of the stream (km/h)

From the information we have:
1. Downstream speed: \( v = x + y = 6 \) km/h
2. Upstream speed: \( u = x - y = 2 \) km/h

### Step 5: Solve the Equations
We have two equations:
1. \( x + y = 6 \)
2. \( x - y = 2 \)

Now, we can solve these equations simultaneously.

### Step 6: Subtract the Second Equation from the First
Subtract the second equation from the first:
\[ (x + y) - (x - y) = 6 - 2 \]
This simplifies to:
\[ 2y = 4 \]
Thus, we find:
\[ y = 2 \text{ km/h} \]

### Step 7: Conclusion
The velocity of the stream is 2 km/h.