The speeds of a boat upstream and downstream are 3 km/h and 13 km/h respectively. Find the speed of stream.

Options

A. 6 kmph
B. 5 kmph
C. 4 kmph
D. 8 kmph

Answer

To find the speed of the stream, we can use the information provided about the speeds of the boat upstream and downstream. Let's denote:

- Speed of the boat in still water = \( x \) km/h
- Speed of the stream = \( y \) km/h

From the problem, we know:

1. The speed of the boat upstream (against the stream) is given by:
\[ x - y = 3 \quad \text{(Equation 1)} \]

2. The speed of the boat downstream (with the stream) is given by:
\[ x + y = 13 \quad \text{(Equation 2)} \]

Now we can solve these two equations step by step.

### Step 1: Add the two equations
We will add Equation 1 and Equation 2 to eliminate \( y \):
\[ (x - y) + (x + y) = 3 + 13 \]
This simplifies to:
\[ 2x = 16 \]

### Step 2: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{16}{2} = 8 \quad \text{(Speed of the boat in still water)} \]

### Step 3: Substitute \( x \) back into one of the equations
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 8 - y = 3 \]

### Step 4: Solve for \( y \)
Rearranging the equation gives:
\[ y = 8 - 3 = 5 \quad \text{(Speed of the stream)} \]

### Final Answer
The speed of the stream is \( 5 \) km/h.

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