Corrections are below in red. Good job! These are tricky words.
Your English instructor, Fon 

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I have had some problems with my colleague. When we did a system development project 2 years ago, W we argued about who was responsible for the project delay. In the case of project, T there were many interfaces within subsystems but roles and responsibilities had not been defined clearly about the job. When we were in testing phase, we got to know that there was were much many remaining works to do. We argued about whose responsiblities the remaining jobs were. My colleague was stubborn and hot tempered. I thought that he was not easy to work with. After arguing, I realized that arguing was no help for solving the problem. I suggested that we should share works and we had several meetings for solving the problem. We had to work overtime to catch up on the project schedule. f Finally, We finished the project on time. After the project I realized that communication management was very important in project. Currently, I get along with him. I try to share the progress of work and communicate with colleagues.