Let's break down the information given:
1. Emily leaves her house 30 seconds after 8:25 AM.
2. The distance from Emily's house to her school is 4.25 miles.
3. At exactly 8:30 AM, Emily passes the post office, which is 3/4 miles away from her house.
4. Emily must arrive at school no later than 8:51 AM to be on time for her first class at 9:00 AM.
To calculate the time it takes for Emily to bike from her house to the post office, we need to know her biking speed. Without that information, it's difficult to determine her exact arrival time at school.
However, let's assume a constant biking speed and calculate the time it takes for Emily to reach the post office:
Distance from house to post office = 3/4 miles
Time taken to reach the post office = 5 minutes (from 8:25 AM + 5 minutes = 8:30 AM)
Now, let's calculate the remaining distance from the post office to the school:
Remaining distance = Total distance - Distance to post office
Remaining distance = 4.25 miles - 3/4 miles = 3.5 miles
If Emily has to cover 3.5 miles, we can't determine her arrival time without knowing her biking speed. The biking speed is necessary to calculate the time taken to cover the remaining distance.
However, if we assume a biking speed of, for example, 10 miles per hour, we can calculate the time taken to cover the remaining 3.5 miles:
Time taken = Distance / Speed
Time taken = 3.5 miles / 10 miles per hour = 0.35 hours = 21 minutes
Adding this time to the previous time (8:30 AM), we get:
8:30 AM + 21 minutes = 8:51 AM
So, if Emily maintains a biking speed of 10 miles per hour, she will arrive at school at exactly 8:51 AM, which is on time for her first class at 9:00 AM.