A car cross a man walking ta 6 km/h the man can see the things up to 450 m only in one direction due to fog.He sees the car which was going in the same direction for 4.5 minutes What is the speed of the car?

Options

A. 9 km/h
B. 12 km/h
C. 12.5 km/h
D. 15 km/h

Answer

To solve the problem, we need to determine the speed of the car given that it crosses a man walking at 6 km/h in the same direction and that the man can see the car for 4.5 minutes within a visibility range of 450 meters.

### Step-by-Step Solution:

1. **Convert the man's speed into meters per minute:**
The man walks at a speed of 6 km/h. To convert this speed into meters per minute, we use the conversion factors:
\[ 6 \text{ km/h} = 6 \times 1000 \text{ m/h} = 6000 \text{ m/h} \]
Since there are 60 minutes in an hour:
\[ \text{Speed in m/min} = \frac{6000 \text{ m}}{60 \text{ min}} = 100 \text{ m/min} \]

**Hint:** Remember to convert kilometers to meters and hours to minutes when changing units.

2. **Calculate the distance the man walks in 4.5 minutes:**
Using the speed of the man, we can find out how far he walks in 4.5 minutes:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 100 \text{ m/min} \times 4.5 \text{ min} = 450 \text{ m} \]

**Hint:** Distance can be calculated using the formula: Distance = Speed × Time.

3. **Determine the total distance the car travels in the same time:**
The car is also traveling during the same 4.5 minutes. Since the man can see the car for 450 meters, we can infer that the car must have traveled at least this distance in the same time frame.

**Hint:** The car must travel at least the distance that the man can see, which is 450 meters.

4. **Set up the equation for the car's speed:**
Let the speed of the car be \( x \) km/h. To convert this speed into meters per minute, we use:
\[ x \text{ km/h} = \frac{x \times 1000 \text{ m}}{60 \text{ min}} = \frac{1000x}{60} \text{ m/min} \]
The distance traveled by the car in 4.5 minutes is:
\[ \text{Distance} = \frac{1000x}{60} \times 4.5 \]

5. **Set the distances equal to each other:**
Since the car travels the same distance as the man can see (450 m), we can set up the equation:
\[ \frac{1000x}{60} \times 4.5 = 450 \]

6. **Solve for \( x \):**
Simplifying the equation:
\[ \frac{1000x \times 4.5}{60} = 450 \]
\[ 1000x \times 4.5 = 450 \times 60 \]
\[ 1000x \times 4.5 = 27000 \]
\[ 1000x = \frac{27000}{4.5} \]
\[ 1000x = 6000 \]
\[ x = \frac{6000}{1000} = 6 \text{ km/h} \]

### Final Answer:
The speed of the car is **6 km/h**.