Look! There is no excuse: you must be to work on time. You are counting on the the full slate of hours to get your full paycheck. You signed a contract with your boss to arrive at a certain time. Your coworker is relying on you relieving her. More than likely, if you work in a hospital, she is comleting a 12 hour shift, and is tired and ready to go home. If you don't show up, if you have a bad track record, then that just ads to this person's stress. Likewise, being late adds to the stress of your boss. So don't be a dunderhead, and show up for work on time. Or, as General Patton said: "If you're ten minutes early you're on time, if you're on time you're late."
Consider this an RT Cave Rule: "Be to work on time."