The calculated distance (air line) between Umm as Summāq and Wādī Mūsá is approximately 110 miles respectively 178 kilometers.
By car or train, the actual journey to Wādī Mūsá is certainly longer, as only the direct route (as the crow flies) between Umm as Summāq and Wādī Mūsá has been calculated here.
Air line (approximately)
178 kilometers
96 nautical miles