Question

Two trains running at constant speed between Jamshedpur and Kolkata take 3 hours and 4 hours respectively. The train from Jamshedpur halves its speed after running for one hour. How much total time do the trains take to meet?

• A. 1 hour
• B. 1.5 hours
• C. 2 hours
• D. 2.5 hours

Hint:

When trains move towards each other, add their speeds and track speed changes carefully after each time segment.

Answer 1

The Correct Option is B

Step 1: Assume total distance.
Let the distance between Jamshedpur and Kolkata be \( D \).
Speed of Train A \( = \dfrac{D}{3} \), Speed of Train B \( = \dfrac{D}{4} \).
Step 2: Distance covered in first one hour.
In 1 hour, Train A covers \( \dfrac{D}{3} \) and Train B covers \( \dfrac{D}{4} \).
Total distance covered \( = \dfrac{D}{3} + \dfrac{D}{4} = \dfrac{7D}{12} \).
Remaining distance \( = D - \dfrac{7D}{12} = \dfrac{5D}{12} \).
Step 3: Speed after halving.
New speed of Train A \( = \dfrac{D}{6} \).
Combined speed now \( = \dfrac{D}{6} + \dfrac{D}{4} = \dfrac{5D}{12} \).
Step 4: Time to cover remaining distance.
Time \( = \dfrac{\frac{5D}{12}}{\frac{5D}{12}} = 1 \) hour.
Step 5: Total time.
Total time \( = 1 + 0.5 = 1.5 \) hours.
Final Answer:
\[ \boxed{1.5 \text{ hours}} \]