When two trains start traveling towards each other, the sum of the distance covered by them when they meet is equal to the distance between them at the start of their journey.
Let d1= Distance covered by Train A
d2 = Distance covered by Train B
d1+d2 = 190
Let time taken by train B to meet Train A be t hrs.
Since Train A travels 1 hr more than Train B, time taken by train A to meet Train B = (t+1) hrs
d1+d2=190
15*(t+1)+10*t=190
15t+15+10t=190
25t=175
t=7
Hence, train A traveled for 15*(7+1)=120 km

Here,

Since the train A started 1 hour before train B, hence in 1 hr, Train A travelled = 15 miles,

Now Train A and Train B are 190 - 15 = 175 miles apart.

The time required to meet = 17515+1017515+10 = 77 hr

Hence the Train A travelled = 15+(15∗7)15+(15∗7) = 120 miles

Thanks You!

Since train A travelled 1hr before train B, then the distance between both trains will reduce by 15miles (train A travels 15mph) to give 190 - 15 = 175.
Now the speed of both trains will be added since they're travelling toward each other to give 15 + 10 = 25mph.
Hence the travel time of both trains will be given as T = d/s where d = 175m and speed = 25mph. 175/25 = 7hrs.
As such the distance travelled by train A is given as d = t * s where t = 7, s = 15 to get 7 * 15 = 105miles. But remember train A had a 15miles 1hr head start, thus 105 + 5 = 120miles.