Two trains starting at the same time from two stations, 200 km apart and going in opposite directions, cross each other at a distance of 110 km from one of them. What is the ratio of their speeds?

Options

A. `11:20`
B. `9:20`
C. `11:9`
D. `19:20`

Answer

To solve the problem, we need to determine the ratio of the speeds of the two trains based on the distances they traveled before crossing each other.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two trains starting from two stations that are 200 km apart.
- They are moving in opposite directions and meet at a point that is 110 km from one station.

2. **Identifying Distances**:
- Let’s denote the stations as A and B.
- The distance from station A to the meeting point is 110 km.
- Therefore, the distance from station B to the meeting point is:
\[ 200 \text{ km} - 110 \text{ km} = 90 \text{ km} \]

3. **Using the Concept of Speed and Time**:
- Let the speed of train A be \( S_A \) and the speed of train B be \( S_B \).
- Since both trains start at the same time and meet at the same time, the time taken by both trains to reach the meeting point is the same. We can denote this time as \( t \).

4. **Setting Up the Equations**:
- For train A:
\[ \text{Distance} = \text{Speed} \times \text{Time} \implies 110 = S_A \times t \implies S_A = \frac{110}{t} \]
- For train B:
\[ \text{Distance} = \text{Speed} \times \text{Time} \implies 90 = S_B \times t \implies S_B = \frac{90}{t} \]

5. **Finding the Ratio of Speeds**:
- Now we can find the ratio of the speeds of the two trains:
\[ \frac{S_A}{S_B} = \frac{\frac{110}{t}}{\frac{90}{t}} = \frac{110}{90} = \frac{11}{9} \]

6. **Conclusion**:
- The ratio of the speeds of the two trains is:
\[ \text{Ratio of speeds} = \frac{11}{9} \]