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 Question:
Two trains start at the same time from opposite points (B and C) and move towards each other. After they cross paths, we are given the time each train takes to complete the rest of its journey. We need to find the ratio of their speeds.
Step 2: Key Formula or Approach:
There is a standard formula for this specific scenario. If two objects start at the same time from points A and B towards each other, and after meeting they take times \(t_1\) and \(t_2\) respectively to reach B and A, then 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 Explanation:
Let's denote the train from C to B as Train 1 and the train from B to C as Train 2.
Let the speed of Train 1 be \(s_1\).
Let the speed of Train 2 be \(s_2\).
After meeting, the time taken by Train 1 to reach its destination (B) is \(t_1 = 4\) hours.
After meeting, the time taken by Train 2 to reach its destination (C) is \(t_2 = 9\) hours.
Using the formula:
\[ \frac{s_1}{s_2} = \sqrt{\frac{t_2}{t_1}} \] Substitute the given values:
\[ \frac{s_1}{s_2} = \sqrt{\frac{9}{4}} \] \[ \frac{s_1}{s_2} = \frac{3}{2} \] The ratio of the speed of Train 1 to the speed of Train 2 is 3:2.
Step 4: Final Answer:
The ratio of their speeds is 3:2.