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
• E.

Hint:

Remember the Inverse Square Root rule for this specific "after meeting" scenario. The train that takes less time after meeting is the faster one. Since 4 < 9, the first train must be faster.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
There is a specific mathematical relationship for two objects moving toward each other that meet and then take different times to reach their opposite starting points.

Step 2: Key Formula or Approach
If two trains start at the same time and after meeting, they take $t_1$ and $t_2$ time to reach their destinations, the ratio of their speeds ($s_1$ and $s_2$) is given by: \[ \frac{s_1}{s_2} = \sqrt{\frac{t_2}{t_1}} \]

Step 3: Detailed Calculation
1. Let the time taken by the first train after meeting be $t_1 = 4$ hours. 2. Let the time taken by the second train after meeting be $t_2 = 9$ hours. 3. Ratio of speeds: \[ \frac{s_1}{s_2} = \sqrt{\frac{9}{4}} \] \[ \frac{s_1}{s_2} = \frac{3}{2} \]

Step 4: Final Answer
The ratio of their speeds is 3:2.