A metro leaves after every 15 minutes. A person is running towards metro then he catches the metro after 12 minutes. If speed of metro is 16 km/h. Find speed of man.

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the problem
The metro leaves every 15 minutes and a person catches the metro after running for 12 minutes. The speed of the metro is given as 16 km/h. We need to find the speed of the person.

### Step 2: Convert the time into hours
Since the speed of the metro is given in km/h, we need to convert the time the person runs (12 minutes) into hours.
\[ \text{Time in hours} = \frac{12 \text{ minutes}}{60} = \frac{1}{5} \text{ hours} \]

### Step 3: Calculate the distance covered by the metro in 12 minutes
The metro travels for 12 minutes while the person is running. We can calculate the distance covered by the metro in that time.
\[ \text{Distance} = \text{Speed} \times \text{Time} = 16 \text{ km/h} \times \frac{1}{5} \text{ hours} = \frac{16}{5} \text{ km} = 3.2 \text{ km} \]

### Step 4: Calculate the distance the metro would cover in 15 minutes
The metro leaves every 15 minutes, so we can calculate how far the metro would have traveled in that time.
\[ \text{Distance in 15 minutes} = 16 \text{ km/h} \times \frac{15}{60} = 16 \text{ km/h} \times \frac{1}{4} \text{ hours} = 4 \text{ km} \]

### Step 5: Determine the distance the person needs to cover
The person needs to cover the distance between the metro that left 15 minutes ago and the metro that he catches after 12 minutes. The distance is:
\[ \text{Distance to cover} = \text{Distance covered by metro in 15 minutes} - \text{Distance covered by metro in 12 minutes} \]
\[ \text{Distance to cover} = 4 \text{ km} - 3.2 \text{ km} = 0.8 \text{ km} \]

### Step 6: Calculate the speed of the person
Now, we can find the speed of the person using the distance he covered and the time he took.
\[ \text{Speed of the person} = \frac{\text{Distance}}{\text{Time}} = \frac{0.8 \text{ km}}{\frac{1}{5} \text{ hours}} = 0.8 \text{ km} \times 5 = 4 \text{ km/h} \]

### Final Answer
The speed of the man is **4 km/h**.

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