### Home > CC4 > Chapter 10 > Lesson 10.1.1 > Problem10-12

10-12.

Write and solve an absolute value inequality for this situation. Homework Help ✎

The accuracy of a certain stopwatch varies by 5%, meaning that the time it shows may be off as much as 5% from the actual time. If the stopwatch shows a time of 3:26 (3 minutes, 26 seconds) for an athlete’s 800m run, then x is the actual time and 0.05x is the potential amount of error. Use this information to write your equation and determine the range of possible times that the run may actually have taken.

Convert the minutes-seconds into just seconds.

$\text{Since 3:26 is 206 seconds, the inequality that represents this information is: }\left | \textit{x}-206 \right |\leq .05\textit{x}$

The range of possible times is 196.19 seconds to 216.84 seconds.
Which is 3:16.2 to 3:36.8.