A train travels 40 percent faster than a car. Both start from point A at the same time and reach point B, which is 140 km away, at exactly the same time. On the way, the train stops for a total of 25 minutes at stations. What is the speed (in km/h) of the train?

Introduction / Context:
This problem compares the motion of a car and a train travelling the same distance between two points. The train is faster but has stoppage time at stations. The key idea is that despite different speeds and stops, both reach the destination simultaneously. We use this time equality to determine the train speed.

Given Data / Assumptions:

• Distance from A to B = 140 km.
• Train travels 40 percent faster than the car.
• Train stops for a total of 25 minutes.
• Both start together from point A and reach point B at the same moment.
• Speeds are constant when each vehicle is moving.

Concept / Approach:
Let v be the speed of the car in km/h. Then the train speed is 1.4 * v because it is 40 percent faster. Car travel time is distance divided by its speed. Train travel time has two parts: actual running time plus stoppage time. Since arrival times are equal, their total times must match. We convert stoppage time to hours, form an equation in v, solve for v, and then compute the train speed as 1.4 * v.

Step-by-Step Solution:
Step 1: Let speed of car be v km/h. Step 2: Speed of train = 1.4 * v km/h. Step 3: Time taken by car = 140 / v hours. Step 4: Running time of train (without stops) = 140 / (1.4 * v) hours. Step 5: Simplify running time: 140 / (1.4 * v) = 100 / v hours. Step 6: Stoppage time for train = 25 minutes = 25 / 60 hours = 5 / 12 hours. Step 7: Total time for train = 100 / v + 5 / 12 hours. Step 8: Since both reach together, 140 / v = 100 / v + 5 / 12. Step 9: Subtract: (140 / v) - (100 / v) = 5 / 12, so 40 / v = 5 / 12. Step 10: Solve for v: v = 40 * 12 / 5 = 96 km/h. Step 11: Train speed = 1.4 * 96 = 134.4 km/h.

Verification / Alternative check:
Car time = 140 / 96 hours which is about 1.458 hours. Train running time is 100 / 96 which is about 1.0417 hours. Adding stoppage time 5 / 12 (about 0.4167) gives 1.4584 hours, approximately equal to car time, allowing for rounding. This confirms that the train speed 134.4 km/h satisfies the condition that both arrive together.

Why Other Options Are Wrong:

• 67 km/h: This is far too slow given that the train is faster than the car and still must make up for stoppages.
• 145.9 km/h and 160 km/h: These speeds would make the train arrive significantly earlier even after stopping 25 minutes, contradicting the requirement that both arrive at the same time.

Common Pitfalls:
A common mistake is to forget to convert stoppage time from minutes to hours or to treat the 40 percent faster condition incorrectly by adding a fixed value instead of a percentage of the car speed. Some learners also misinterpret the phrase reach at the same time and try to balance distances instead of times. Always equate total travel times when two journeys end together.

Final Answer:
The speed of the train is 134.4 km/h.