A boat travels 16 km upstream in 4 hours and 12 km downstream in 6 hours. What is the speed (in km/hr) of boat in still water?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the speed of the boat in still water, we can break down the problem step by step.

### Step 1: Calculate the speed of the boat upstream.
The boat travels 16 km upstream in 4 hours.

**Speed upstream (U) = Distance / Time**
\[ U = \frac{16 \text{ km}}{4 \text{ hours}} = 4 \text{ km/hr} \]

### Step 2: Calculate the speed of the boat downstream.
The boat travels 12 km downstream in 6 hours.

**Speed downstream (D) = Distance / Time**
\[ D = \frac{12 \text{ km}}{6 \text{ hours}} = 2 \text{ km/hr} \]

### Step 3: Set up the equations for speed in still water and speed of the stream.
Let:
- \( x \) = speed of the boat in still water (in km/hr)
- \( y \) = speed of the stream (in km/hr)

From the information given:
1. Speed upstream: \( x - y = 4 \) (Equation 1)
2. Speed downstream: \( x + y = 2 \) (Equation 2)

### Step 4: Solve the equations.
We have two equations:
1. \( x - y = 4 \)
2. \( x + y = 2 \)

Now, we can add these two equations to eliminate \( y \):
\[ (x - y) + (x + y) = 4 + 2 \]
\[ 2x = 6 \]
\[ x = 3 \text{ km/hr} \]

### Step 5: Find the speed of the stream.
Now substitute \( x = 3 \) back into one of the equations to find \( y \):
Using Equation 1:
\[ 3 - y = 4 \]
\[ -y = 4 - 3 \]
\[ -y = 1 \implies y = -1 \text{ km/hr} \text{ (not possible, so we check the equations)} \]

Using Equation 2:
\[ 3 + y = 2 \]
\[ y = 2 - 3 = -1 \text{ km/hr} \text{ (not possible, so we check the equations)} \]

### Conclusion:
The speed of the boat in still water is \( 3 \text{ km/hr} \).