The calculated distance (air line) between Ingelheim am Rhein and Gelsenkirchen is approximately 114 miles respectively 184 kilometers.
By car or train, the actual journey to Gelsenkirchen is certainly longer, as only the direct route (as the crow flies) between Ingelheim am Rhein and Gelsenkirchen has been calculated here.
Air line (approximately)
184 kilometers
99 nautical miles