Question

Two trains run simultaneously, one of which is traveling from place C to B and the other is traveling from place B to C. After meeting, the two trains arrive at their destinations in 4 hours and 9 hours respectively. Find the ratio of their speeds.

• A. 4:3
• B. 4:5
• C. 3:2
• D. 3:4
• E. 2:3

Hint:

Remember that speed and time are inversely proportional. In the meeting-point formula, the time for the second train goes in the numerator to find the ratio of the first train's speed.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a standard problem involving two objects moving towards each other. There is a specific mathematical relationship between the speeds of the objects and the time taken to reach their respective destinations after they meet. 
Step 2: Key Formula or Approach: 
If two objects $A$ and $B$ start at the same time from opposite points and after meeting take \(t_1\) and \(t_2\) hours to reach their destinations, the ratio of their speeds is:

\[ \frac{\text{Speed of A}}{\text{Speed of B}} = \sqrt{\frac{t_2}{t_1}} \] 
Step 3: Detailed Explanation: 
1. Identify the given times:

- Time taken by the first train (C to B) after meeting: \(t_1 = 4\) hours.

- Time taken by the second train (B to C) after meeting: \(t_2 = 9\) hours.

2. Apply the ratio formula: \[ \frac{S_1}{S_2} = \sqrt{\frac{9}{4}} \] 3. Simplify the square root: \[ \frac{S_1}{S_2} = \frac{3}{2} \] The ratio of their speeds is 3:2. 
Step 4: Final Answer: 
The ratio of the speeds of the two trains is 3:2.