A carriage driving in a fog passed a man who was walking at the speed of 3 km/hr in same direction the man could see the carriage for 4 min & it was visible to him upto a distance of 100 m. What was the speed of the carriage ?

Options

A. a)45 km/hr
B. b)4.5 km/hr
C. c)35 km/hr
D. d)3.5 km/hr

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the distance traveled by the man in 4 minutes.
- The speed of the man is given as 3 km/hr.
- We need to convert the time from minutes to hours since the speed is in km/hr.
- 4 minutes = \( \frac{4}{60} \) hours = \( \frac{1}{15} \) hours.

**Distance = Speed × Time**
- Distance traveled by the man = \( 3 \text{ km/hr} \times \frac{1}{15} \text{ hr} = \frac{3}{15} \text{ km} = \frac{1}{5} \text{ km} = 200 \text{ meters} \).

### Step 2: Determine the total distance over which the carriage was visible.
- The man could see the carriage for 4 minutes, and it was visible to him up to a distance of 100 meters.
- Therefore, the total distance covered by the carriage while the man could see it = Distance traveled by the man + Distance the carriage was visible = 200 meters + 100 meters = 300 meters.

### Step 3: Convert the total distance into kilometers.
- Total distance = 300 meters = \( \frac{300}{1000} \) km = 0.3 km.

### Step 4: Calculate the speed of the carriage.
- We know the total distance covered by the carriage is 0.3 km in 4 minutes.
- We need to convert the time from minutes to hours for speed calculation.
- 4 minutes = \( \frac{4}{60} \) hours = \( \frac{1}{15} \) hours.

**Speed = Distance / Time**
- Speed of the carriage = \( \frac{0.3 \text{ km}}{\frac{1}{15} \text{ hr}} = 0.3 \times 15 = 4.5 \text{ km/hr} \).

### Final Answer:
- The speed of the carriage is **4.5 km/hr**.

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