Let the speed of the express be e, and log the local train be s.

The time that the express takes is t_e = 250/e, and the time the local train takes is t_s = 250/s. As s = e - 10 we are left with:

t_e = 250/e,

and

t_s = 250/(e-10).

We are also told that:

t_e = t_s - 1.25,

so we have:

250/e = 250/(e-10) - 1.25.

Multiply through by e(e-10) to get:

250 (e-10) = 250 e - 1.25 e (e-10)

which simplifies to the quadratic:

1.25 e^2 - 12.5 e - 2500 = 0,

which has roots e=50 and e=-40, but as e should be positive we find

e=50.

RonL