Data:
Total distance: 450 miles
Total time: 8 h
Average 60 mi/h before noon
Average 50 mi/h afternoon
The relationship between the time, speed (average) and distance is drescribed in the next equations:

Then, if you multiply the speed and the time you get the distance:
time before noon: b
time afternoon: a

The sum of a and b is the total time:

Use the next system of equations to find a and b:

1. Solve a in the second equation:

2. Substitute the a in first equation by the value you get in first step:

3. Solve b:

4. Use the value of b=5 to solve a:

Then, Jaron begin his trip 5 hours before noon ( at 7:00) and end it 3 hours afternoon (at 15:00)