After pulling a couple of levers and causing a minor cave-in you'll come across a rather angry miner. You'll need your entire group blown up by the same stick of dynamite. The easiest way to do this is regroup everybody on the right of the bridge, and just wait for the boom stick!
A couple of notes here. Firstly, if you're looking to get Creamed Corn then you should ensure the can of corn the miner throws at you is blown up by dynamite. Otherwise you'll have to take it with you and find another way of destroying it.
Secondly, you should aim to get blown up before you begin solving the mine car puzzles. Once all three cars are delivered he'll stop throwing dynamite.