The distance between A & B is 211 km. One boat starts moving from point A towards B in downstream at 7 : 45 am. After on hour, another boat starts from the point B towards A. At 12 : 45 pm both boat will meet. If speed of boat first and second is 26 km/hr. and 18 km/hr. respectively in still water. Then find the speed of stream.

Options

A. 9 km/hr
B. 6 km/hr
C. 10 km/hr
D. 12 km/hr

Answer

To solve the problem, we need to determine the speed of the stream given the distances and speeds of two boats traveling towards each other. Here's a step-by-step solution:

### Step 1: Understand the time of travel for each boat
- The first boat starts from A at 7:45 AM and travels downstream.
- The second boat starts from B at 8:45 AM and travels upstream.
- They meet at 12:45 PM.

### Step 2: Calculate the time each boat travels
- The first boat travels from 7:45 AM to 12:45 PM, which is 5 hours.
- The second boat travels from 8:45 AM to 12:45 PM, which is 4 hours.

### Step 3: Define the speeds of the boats
- Speed of the first boat in still water = 26 km/hr (downstream).
- Speed of the second boat in still water = 18 km/hr (upstream).
- Let the speed of the stream be \( S \) km/hr.

### Step 4: Calculate the effective speeds of the boats
- Effective speed of the first boat (downstream) = \( 26 + S \) km/hr.
- Effective speed of the second boat (upstream) = \( 18 - S \) km/hr.

### Step 5: Write the equation for the total distance covered
The total distance between A and B is 211 km. The distance covered by both boats when they meet can be expressed as:
\[ \text{Distance by first boat} + \text{Distance by second boat} = 211 \text{ km} \]
This can be written as:
\[ (26 + S) \times 5 + (18 - S) \times 4 = 211 \]

### Step 6: Expand and simplify the equation
Expanding the equation gives:
\[ (130 + 5S) + (72 - 4S) = 211 \]
Combining like terms:
\[ 130 + 72 + 5S - 4S = 211 \]
\[ 202 + S = 211 \]

### Step 7: Solve for the speed of the stream
Subtract 202 from both sides:
\[ S = 211 - 202 \]
\[ S = 9 \text{ km/hr} \]

### Final Answer
The speed of the stream is **9 km/hr**.

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