Question

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

• A. 11 : 45 am
• B. 10 : 45 am
• C. 11 : 20 am
• D. 11 : 00 am

Answer 1

The Correct Option is D

The problem involves determining when two trains meet. Let's break it down into steps:

1. Calculate the initial head start: Train A departs at 9:00 am moving at 40 km/hr. By the time Train B departs at 10:30 am, Train A would have traveled for 1.5 hours.
   Distance covered by Train A = speed × time = 40 km/hr × 1.5 hr = 60 km.
2. Determine the remaining distance: The total distance between the stations is 90 km. Therefore, the remaining distance when Train B starts is 90 km - 60 km = 30 km.
3. Calculate the relative speed: Train A and Train B move towards each other at speeds of 40 km/hr and 20 km/hr, respectively. Combined (relative) speed = 40 km/hr + 20 km/hr = 60 km/hr.
4. Calculate time required to meet: Using the formula time = distance/speed,
   Time = 30 km / 60 km/hr = 0.5 hr = 30 minutes.
5. Find the meeting time: Train B starts at 10:30 am and takes 30 minutes to meet Train A, thus the trains meet at 11:00 am.

The trains meet at 11:00 am.

Answer 2

Step 1: Distance Covered by A

From 9:00 AM to 10:30 AM = 1.5 hours. Speed of A = 40 km/h. So, distance covered by A: \[ = \frac{3}{2} \times 40 = 60 \text{ km} \]

Step 2: Distance Between A and B at 10:30 AM

Since total distance between them is 90 km, Remaining distance between A and B = \[ 90 - 60 = 30 \text{ km} \]

Step 3: Let them meet after \( t \) hours from 10:30 AM

Relative distance covered: \[ 40t + 20t = 30 \Rightarrow 60t = 30 \Rightarrow t = \frac{1}{2} \text{ hour} \]

Step 4: Meeting Time

\[ \frac{1}{2} \text{ hour} = 30 \text{ minutes} \] So they meet at: \[ 10:30 \text{ AM} + 30 \text{ min} = \boxed{11:00 \text{ AM}} \]

Final Answer:

The correct option is (D): \[ \boxed{11:00 \text{ AM}} \]