Abstract: A trailer-mounted drilling rig incorporates a dual top drive apparatus and a plurality of lifting assemblies useable for decreasing connection time of pipe segments useable during well drilling or other well operations, and methods of connecting pipe segments useable during well drilling or other operations. The plurality of lifting assemblies operatively connected to the dual top drive apparatus and a first lifting assembly is capable of moving a first top drive vertically inline with a wellbore while a second lifting assembly is capable of independently moving a second top drive vertically out of alignment with the wellbore.