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.

From 8:25 am to 30 seconds past 8:29 am, there are 4.5 minutes. Her speed is calculated by dividing the distance of the post office from her house by the time. 
                               speed = 0.75 mile / 4.5 minutes = 1/6 mile / minute
Then, determining the number of minutes she will have to take in order to reach school,
                                  time = 3.42 mile / (1/6 mile/minute) = 20.52 minutes
Adding this to the initial time,
                                final time = 8:25 am + 20.52 minutes
                                                = 8:45 am and 31.2 seconds. 

She will reach the school on time even without increasing her speed.