Emily leaves her house at exactly 8: 25 am to bike to her school, which is 3.42 miles away. when she passes the post office, which is 3/4 mile away from her home, she looks at her watch and sees that it is 30 seconds past 8: 29 am. if emily's school starts at 8: 50 am can emily make it on time without increasing her rate of speed? show and/or explain the work necessary to support your answer.

The speed of Emily is assumed to be constant and is calculated by dividing the distance she traveled from her home to the post office by the time.
                         speed = (0.75 mile) / (4.5 minutes) = 1/6 miles/minute
Then, calculate the time it will take her to travel from home to school.
                  time = (3.42 miles) / (1/6 miles/minute) = 20.52 minutes
Adding this to 8:25 will give us an answer of 8:45:31 am. Thus, she will not be late. 

The answer is option c.