What is the difference beteween 并 and 和 in sentence (S. V. and V.)? What is the difference beteween 并 and 和 in sentence (S. V. and V.)? Which one is correct. E.g.:


  我们在一起跑步(并/和)参加了铁人三项赛
We don't usually use 并/和 to interpret (S. V. and V.) in English if two actions are not really relevant. Instead, we can use 又...又... 

For example, 


We sing and dance： 我们又唱又跳。 Not 我们唱 并/和 跳. 
We eat and drink. = 我们又吃又喝。 not 我们吃 并/和 喝.


However, we use 和(not 并) to interpret (S. and S. + V.) and (S + V + O. and O.). 

For example,


他和我去买东西。： he and I go shopping. 
我吃苹果和香蕉。： I eat apple and banana. 


并 is short for 并且, and could be used as conjunction, meaning 'and'. It often connects the two sentences or clauses. It could also connect two verbs if the two actions are logically relevant. (S. + V. and V. + O. ) 

For example,


我完全赞成并乐于接受这一安排。 I fully agree to the arrangement and take it delightfully. // connecting two clauses. 
我赞同并接受这个决定。 I agree and accept the decision. // The two actions are relevant in this case. 


In your case, 并 should be used as a conjunction for two clauses. 


  我们在一起跑并参加了铁人三项赛.