Lets say that the speed of fast train =x
and that of slow one= x-20
Time taken by fast train to reach = 250/x
time taken by slow train to reach = 250/(x-20)
Its given that the difference between the starting time is 10minutes
and the total difference of time taken =3hours 30 mins
This gives that the slower train takes a time =250/x + 3hours 20mins
=250/x + 3.33
Thus
250/(x-20) = 250/(x) + 3.33
Solve again.
To learn the general technique for "combined work" exercises, try here.
Once you have learned the basic terms and techniques, the following should make sense:
. . .time to complete job (in minutes):
. . . . .smaller: s
. . . . .larger: s - 5
. . . . .together: 100/9
. . .portion completed (per minute):
. . . . .smaller: 1/s
. . . . .larger: 1/(s - 5)
. . . . .together: 9/100
Add their per-minute completion amounts, set equal to the total per-minute amount, and solve the rational equation. (The first step will be to multiply through to clear the denominators. Then you'll solve the resulting quadratic equation.)