Question

Two trains A and B start simultaneously in the opposite direction from two points A and B and arrive at their destinations 9 and 4 hours respectively after their meeting each other. At what rate does the second train B travel if the first train travels at 80 km per hour.

• A. 100 km/hr
• B. 110 km/hr
• C. 120 km/hr
• D. 130 km/hr
• E. 140 km/hr

Hint:

Memorize the formula \(\frac{S_1}{S_2} = \sqrt{\frac{t_2}{t_1}}\) for problems where two objects start simultaneously, meet, and the times to reach the destination *after meeting* are given. It saves a lot of time compared to deriving it from basic principles.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Two trains start from opposite points, move towards each other, meet at a point, and then continue to their respective destinations. We are given the times they take to complete their journeys *after* meeting and the speed of one train. We need to find the speed of the other train.
Step 2: Key Formula or Approach:
For this specific scenario, there is a standard formula that relates the speeds of the two objects to the time they take to reach their destinations after meeting. If the speeds of train A and B are \(S_A\) and \(S_B\), and the time taken after meeting to reach their destinations are \(t_A\) and \(t_B\) respectively, the formula is: \[ \frac{S_A}{S_B} = \sqrt{\frac{t_B}{t_A}} \] Step 3: Detailed Explanation:
Let's identify the given values:
Speed of the first train (A), \(S_A\) = 80 km/hr.
Time taken by train A after meeting, \(t_A\) = 9 hours.
Time taken by train B after meeting, \(t_B\) = 4 hours.
We need to find the speed of the second train (B), \(S_B\).
Now, substitute the values into the formula: \[ \frac{80}{S_B} = \sqrt{\frac{4}{9}} \] \[ \frac{80}{S_B} = \frac{\sqrt{4}}{\sqrt{9}} \] \[ \frac{80}{S_B} = \frac{2}{3} \] To solve for \(S_B\), we can cross-multiply: \[ 2 \times S_B = 80 \times 3 \] \[ 2 \times S_B = 240 \] \[ S_B = \frac{240}{2} \] \[ S_B = 120 \, \text{km/hr} \] Step 4: Final Answer:
The speed of the second train B is 120 km/hr.