In all cases where public roads, or parts thereof, in townships of this commonwealth, connecting a city with a city, a city with a borough, or a borough with a borough, or connecting one part of a city with another part of the same city, shall have become inconvenient and burdensome, and shall require altering and widening, or either altering or widening, to meet the requirements of public travel thereon, it shall be lawful for the court of quarter sessions, by the same process now provided for opening and laying out public roads, to alter and widen, or either alter or widen, such roads, vacating such part or parts of the said old roads as are rendered useless by such alteration.