Question

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??

Answer 1

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