Two trains cross in electric pole in 16 sec. and 19 sec. respectively. If their speed ratio is 58:32. Then in how much time they will cross each other if they are moving in opposite direction.

Options

A. `18.76` sec
B. `17.06` sec
C. `17.65` sec
D. `17.96` sec

Answer

To solve the problem, we need to find the time taken for two trains to cross each other when they are moving in opposite directions. We will follow these steps:

### Step 1: Determine the speeds of the trains

Let the lengths of the trains be \( L_1 \) and \( L_2 \). The speeds of the trains can be calculated using the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

For Train 1 (crossing the electric pole in 16 seconds):

\[ S_1 = \frac{L_1}{16} \]

For Train 2 (crossing the electric pole in 19 seconds):

\[ S_2 = \frac{L_2}{19} \]

### Step 2: Establish the ratio of speeds

Given the speed ratio \( S_1 : S_2 = 58 : 32 \), we can express the speeds in terms of a common variable \( k \):

\[ S_1 = 58k \quad \text{and} \quad S_2 = 32k \]

### Step 3: Relate the lengths of the trains to their speeds and times

From the speed equations, we can express the lengths of the trains:

\[ L_1 = S_1 \times 16 = 58k \times 16 = 928k \]

\[ L_2 = S_2 \times 19 = 32k \times 19 = 608k \]

### Step 4: Calculate the total distance when trains cross each other

When the two trains cross each other while moving in opposite directions, the total distance they need to cover is the sum of their lengths:

\[ \text{Total Distance} = L_1 + L_2 = 928k + 608k = 1536k \]

### Step 5: Calculate the relative speed of the trains

When moving in opposite directions, the relative speed is the sum of their speeds:

\[ \text{Relative Speed} = S_1 + S_2 = 58k + 32k = 90k \]

### Step 6: Calculate the time taken to cross each other

Using the formula for time, where time is equal to distance divided by speed, we can find the time taken to cross each other:

\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} = \frac{1536k}{90k} \]

The \( k \) cancels out:

\[ \text{Time} = \frac{1536}{90} = 17.0667 \text{ seconds} \approx 17.07 \text{ seconds} \]

### Final Answer

The time taken for the two trains to cross each other when moving in opposite directions is approximately **17.07 seconds**.

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