Let Vs be the velocity of the slower train, and Vf is that of the fast train.

The first statement leads you to

b/Vs - b/Vf = a. Or

1/Vf - 1/Vs = a/b .....(1)

The second statement leads you to

Vf*c - Vf*c = 1 km Or

Vf - Vs = 1/c .........(2)

Vf = Vs + 1/c

Substitute this value of Vf in equation (1) and solve the quadratic to find Vs.