Final answer:
An absolute value equation representing the fastest and slowest times for the track team is |t - 13.06| = 1.8, where t is the time in seconds. This yields times of 11.26 seconds for the fastest and 14.86 seconds for the slowest runners.
Step-by-step explanation:
The student is looking to write an absolute value equation that represents the fastest and slowest times for members of a track team based on their average 100-meter dash time. If the team's average time is 13.06 seconds, and the variation from the average is 1.8 seconds for the slowest and fastest times, we can set up an equation using the definition of absolute value to capture this relationship.
The absolute value of a number is the distance of that number from 0 on a number line, without considering which direction from zero the number lies. Since both the fastest and slowest times are 1.8 seconds away from the average, we can write this relationship as |t - 13.06| = 1.8, where t represents the time.
The times that satisfy this equation will be 13.06 - 1.8 = 11.26 seconds and 13.06 + 1.8 = 14.86 seconds, representing the fastest and slowest times respectively.