`{:("Column A" , "A train takes 15 second to cross a","ColumnB"),( , "bridge at 50 mph,and at the same",),( , "speed takes 10 seconds to cross",),( , "the same bridge when the train's length is halved",),("Length of the bridge"," ","Original length of the train"):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided.

### Step 1: Define Variables
Let:
- \( L \) = Length of the train
- \( B \) = Length of the bridge

### Step 2: Set Up the First Equation
The train takes 15 seconds to cross the bridge at a speed of 50 mph. The total distance covered while crossing the bridge is the length of the bridge plus the length of the train, which can be expressed as:
\[ \text{Distance} = B + L \]
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
We can write:
\[ 50 = \frac{B + L}{15} \]
Multiplying both sides by 15 gives us:
\[ B + L = 750 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
When the length of the train is halved, it takes 10 seconds to cross the bridge at the same speed. The distance covered in this case is:
\[ \text{Distance} = B + \frac{L}{2} \]
Using the speed formula again:
\[ 50 = \frac{B + \frac{L}{2}}{10} \]
Multiplying both sides by 10 gives us:
\[ B + \frac{L}{2} = 500 \quad \text{(Equation 2)} \]

### Step 4: Solve the Equations
Now we have two equations:
1. \( B + L = 750 \)
2. \( B + \frac{L}{2} = 500 \)

From Equation 1, we can express \( L \) in terms of \( B \):
\[ L = 750 - B \]

Substituting \( L \) into Equation 2:
\[ B + \frac{750 - B}{2} = 500 \]
Multiplying through by 2 to eliminate the fraction:
\[ 2B + 750 - B = 1000 \]
Simplifying gives:
\[ B + 750 = 1000 \]
Thus:
\[ B = 250 \]

### Step 5: Find the Length of the Train
Now substitute \( B \) back into the equation for \( L \):
\[ L = 750 - 250 = 500 \]

### Step 6: Conclusion
We find that:
- Length of the bridge \( B = 250 \)
- Length of the train \( L = 500 \)

### Final Answer
The length of the train is twice the length of the bridge:
\[ L = 2B \]
Thus, the length of the train is greater than the length of the bridge.