A train of 320 m cross a platform in 24 seconds at the speed of 120 km/h. while a man cross same platform in 4 minute. What is the speed of man in m/s?

Options

A. 2.4
B. 1.5
C. 1.6
D. 2

Answer

To solve the problem step by step, we will first determine the length of the platform using the information provided about the train. Then, we will calculate the speed of the man crossing the platform.

### Step 1: Convert the speed of the train from km/h to m/s
The speed of the train is given as 120 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
Calculating this:
\[ 120 \times \frac{5}{18} = \frac{600}{18} = 33.33 \text{ m/s} \]

**Hint:** Remember that to convert km/h to m/s, multiply by \(\frac{5}{18}\).

### Step 2: Calculate the total distance the train travels while crossing the platform
The total distance covered by the train while crossing the platform is the length of the train plus the length of the platform (let's denote the length of the platform as \(P\)):
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Platform} = 320 + P \]

**Hint:** The total distance covered by the train is the sum of its own length and the length of the platform.

### Step 3: Use the time taken by the train to find the length of the platform
The time taken by the train to cross the platform is given as 24 seconds. We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the known values:
\[ 320 + P = 33.33 \times 24 \]
Calculating the right side:
\[ 33.33 \times 24 = 800 \text{ meters} \]
Thus, we have:
\[ 320 + P = 800 \]
Now, solving for \(P\):
\[ P = 800 - 320 = 480 \text{ meters} \]

**Hint:** Use the formula for distance to relate speed, time, and distance to find the unknown.

### Step 4: Calculate the speed of the man crossing the platform
The man crosses the same platform in 4 minutes. First, we need to convert this time into seconds:
\[ 4 \text{ minutes} = 4 \times 60 = 240 \text{ seconds} \]
Now, we can find the speed of the man using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{480}{240} \]
Calculating this gives:
\[ \text{Speed} = 2 \text{ m/s} \]

**Hint:** To find speed, divide the distance by the time taken.

### Final Answer
The speed of the man is **2 m/s**.