A person is travelling by train and car in his whole journey.. The matter is if he is travelling first by train till 60kms and the rest by car, then his total journey has taken 4 hours.. but if he is travelling first by train till 100kms, then his journey has taken 10 mins more than before.. According to the question, what was the speed of that train??

speed of train = x km/h

speed of car = y km/h
total distance is D km

60/x + (D-60)/y = 4
60y + (D-60)x = 4xy

100/x + (D-100)/y = 4 1/6 = 25/6
100y + (D-100)x = 25/6 xy

you seem to have some missing information, because we have 3 variables, but only 2 equations.

well, let's go as far as we can ...
60y + Dx - 60x = 4xy
Dx = 4xy + 60x - 60y

100y + Dx - 100x = (25/6)xy
Dx = (25/6)xy + 100x - 100y

thus:
4xy + 60y - 60y = (25/6)xy + 100x - 100y
160y - 160x = (1/6)xy
960y - 960x = xy
960y - xy = 960x
y(960 - x) = 960x
y = 960x/(960-x)

At this point you should see my point at the top
suppose we let x = 40, then y = 960/23, D = 164.348
this data fits your conditions, check with a calculator

suppose we let x = 50, then y = 4800/91 , D = 207.69
this also works

so there would be an infinite number of solutions.
just pick any x between 0 and 960

To find the speed of the train, we need to analyze the information provided and use the concept of time, distance, and speed.

Let's assume the speed of the train is 'x' km/h, and the speed of the car is 'y' km/h.

1. In the first scenario when the person travels 60 km by train and the rest by car, the time spent on the journey is 4 hours. We can express this as an equation:

Time taken by the train = Distance traveled by the train / Speed of the train
Time taken by the car = Distance traveled by the car / Speed of the car

We know the total journey time is 4 hours:
Time taken by the train + Time taken by the car = 4

Using the given information, we can form the equation:
60/x + (Total distance - 60)/y = 4

2. In the second scenario, the person travels 100 km by train and the rest by car, taking 10 minutes (or 10/60 hours) longer than before. Therefore, the total journey time is (4 + 10/60) hours.

We can form the equation using the same logic as before:
100/x + (Total distance - 100)/y = 4 + 10/60

Now, we have a system of two equations with two variables (x and y). We can solve these equations simultaneously to find the values of x and y.

By solving these equations, we can find the value of x, which represents the speed of the train.