Using molecular dynamics simulations, we study a liquid model which consists of particles interacting via a spherically-symmetric two-scale Jagla ramp potential with both repulsive and attractive ramps. The Jagla potential displays anomalies similar to those found in liquid water, namely expansion upon cooling and an increase of diffusivity upon compression, as well as a liquid-liquid (LL) phase transition in the region of the phase diagram accessible to simulations. The LL coexistence line, unlike in tetrahedrally-coordinated liquids, has a positive slope, because of the Clapeyron relation, corresponding to the fact that the high density phase (HDL) is more ordered than low density phase (LDL). When we cool the system at constant pressure above the critical pressure, the hydrodynamic properties rapidly change from those of LDL-like to those of HDL-like upon crossing the Widom line. The temperature dependence of the diffusivity also changes rapidly in the vicinity of the Widom line, namely the slope of the Arrhenius plot sharply increases upon entering the HDL domain. The properties of the glass transition are different in the two phases, suggesting that the less ordered phase (LDL) is fragile, while the more ordered phase (HDL) is strong, which is consistent with the behavior of tetrahedrally-coordinated liquids such as water silica, silicon, and BeF$_2$.