A train is moving with a uniform speed. Train crosses a bridge of length 340 meters in 35 seconds and a bridge of length 460 meters in 38 seconds. What is the speed of the train?

Options

A. 72 km/hr
B. 80 km/hr
C. 40 km/hr
D. 144 km/hr

Answer

To find the speed of the train, we can use the information provided about the time taken to cross two bridges of different lengths. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( L \) = Length of the train (in meters)
- \( S \) = Speed of the train (in meters per second)

### Step 2: Set Up Equations
From the first bridge:
- Length of the bridge = 340 meters
- Time taken = 35 seconds

The total distance the train travels while crossing the first bridge is \( L + 340 \) meters. Therefore, we can write the equation:
\[ \frac{L + 340}{35} = S \quad \text{(1)} \]

From the second bridge:
- Length of the bridge = 460 meters
- Time taken = 38 seconds

The total distance the train travels while crossing the second bridge is \( L + 460 \) meters. Therefore, we can write the equation:
\[ \frac{L + 460}{38} = S \quad \text{(2)} \]

### Step 3: Equate the Two Expressions for Speed
Since both expressions equal \( S \), we can set them equal to each other:
\[ \frac{L + 340}{35} = \frac{L + 460}{38} \]

### Step 4: Cross Multiply
Cross multiplying gives us:
\[ 38(L + 340) = 35(L + 460) \]

### Step 5: Expand Both Sides
Expanding both sides:
\[ 38L + 12920 = 35L + 16100 \]

### Step 6: Rearrange the Equation
Rearranging the equation to isolate \( L \):
\[ 38L - 35L = 16100 - 12920 \]
\[ 3L = 3180 \]

### Step 7: Solve for Length of the Train
Dividing both sides by 3:
\[ L = \frac{3180}{3} = 1060 \text{ meters} \]

### Step 8: Substitute Back to Find Speed
Now, substitute \( L \) back into either equation (1) or (2) to find \( S \). Using equation (1):
\[ S = \frac{1060 + 340}{35} = \frac{1400}{35} = 40 \text{ meters/second} \]

### Step 9: Convert Speed to km/h
To convert the speed from meters per second to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):
\[ S = 40 \times \frac{18}{5} = 144 \text{ km/h} \]

### Final Answer
The speed of the train is **144 km/h**.

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