A train can cross a pole in 50 sec. and a 220-meter long bridge in 1 min. Find half the length of train?

Options

A. 500 meters
B. 660 meters
C. 440 meters
D. 550 meters

Answer

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

### Step 1: Understand the Problem
The train crosses a pole in 50 seconds and a 220-meter long bridge in 1 minute (60 seconds). We need to find half the length of the train.

### Step 2: Define Variables
Let:
- \( T \) = Length of the train (in meters)
- \( S \) = Speed of the train (in meters per second)

### Step 3: Set Up the Equations
1. When the train crosses a pole, the distance it covers is equal to its length:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Thus, we have:
\[ T = S \times 50 \quad \text{(1)} \]

2. When the train crosses the bridge, the distance it covers is equal to the length of the train plus the length of the bridge:
\[ T + 220 = S \times 60 \quad \text{(2)} \]

### Step 4: Solve the Equations
From equation (1), we can express speed \( S \) in terms of \( T \):
\[ S = \frac{T}{50} \]

Now substitute \( S \) in equation (2):
\[ T + 220 = \left(\frac{T}{50}\right) \times 60 \]
This simplifies to:
\[ T + 220 = \frac{60T}{50} \]
\[ T + 220 = \frac{6T}{5} \]

### Step 5: Clear the Fraction
To eliminate the fraction, multiply the entire equation by 5:
\[ 5T + 1100 = 6T \]

### Step 6: Rearrange the Equation
Rearranging gives:
\[ 1100 = 6T - 5T \]
\[ 1100 = T \]

### Step 7: Find Half the Length of the Train
Now that we have the length of the train:
\[ T = 1100 \text{ meters} \]
Half the length of the train is:
\[ \frac{T}{2} = \frac{1100}{2} = 550 \text{ meters} \]

### Final Answer
Thus, half the length of the train is **550 meters**.

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