Two trains started at the same time, one from A to B and the other from B to A. If they arrived at B and A respectively 4 hours and 9 hours after they passed each other, the ratio of the speed of the two trains was

Options

A. `2:1`
B. `3:2`
C. `4:3`
D. `5:4`

Answer

To solve the problem, we need to find the ratio of the speeds of the two trains based on the time they take to reach their destinations after passing each other.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Let Train 1 start from A to B and Train 2 start from B to A.
- After they pass each other, Train 1 takes 4 hours to reach B, and Train 2 takes 9 hours to reach A.

2. **Assign Variables**:
- Let the speed of Train 1 be \( S_1 \) and the speed of Train 2 be \( S_2 \).
- The time taken by Train 1 after passing Train 2 to reach B is \( T_1 = 4 \) hours.
- The time taken by Train 2 after passing Train 1 to reach A is \( T_2 = 9 \) hours.

3. **Using the Relation of Speed and Time**:
- The distance covered by Train 1 after passing Train 2 can be expressed as:
\[ \text{Distance}_1 = S_1 \times T_1 = S_1 \times 4 \]
- The distance covered by Train 2 after passing Train 1 can be expressed as:
\[ \text{Distance}_2 = S_2 \times T_2 = S_2 \times 9 \]

4. **Setting Up the Ratio**:
- Since both trains cover the same distance after they pass each other (from the point they meet to their respective destinations), we can set the distances equal:
\[ S_1 \times 4 = S_2 \times 9 \]

5. **Rearranging the Equation**:
- Rearranging the equation gives us:
\[ \frac{S_1}{S_2} = \frac{9}{4} \]

6. **Finding the Ratio**:
- To express this in the form of a ratio, we can write:
\[ S_1 : S_2 = 9 : 4 \]

7. **Conclusion**:
- The ratio of the speeds of Train 1 to Train 2 is \( 9 : 4 \).

### Final Answer:
The ratio of the speed of the two trains is \( 9 : 4 \).

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