The speed of a train is 30 percent more than the speed of a car. Both start from point P at the same time and reach point Q at the same time. P and Q are 130 km apart from each other. On the way, the train stops for 30 minutes at a station. What is the speed of the train?

Given:

Distance between points P and Q: 130 km

Train stops for 30 minutes

Formula:

Speed = Distance/Time

Calculation:

Let's denote the speed of the car as '10x'.

The speed of the train is 30% more than the speed of the car, which can be expressed as 13x 

Now, let's calculate the time taken by the car and the train to travel from point P to Q.

Time is taken by the car: Distance/Speed of the car

Time taken by the train: Distance / Speed of the train + Time spent at the station

The time taken by the car and the train is the same, as mentioned in the question.

Therefore, we can write the equation:

130/10x = 130/(13x) + (30 minutes/60 minutes) [Converting 30 minutes to hours]

To simplify the equation, let's solve it step by step.

130/10x = 130/(13x)  + 1/2

13/x - 10/x = 1/2

x = 6

Speed of the train = 13 × 6 km/h = 78 km/h.

Hence, the speed of the train is 78 km/h.