### Home > INT1 > Chapter 10 > Lesson 10.1.1 > Problem10-12

10-12.

Write and solve an absolute value inequality for this situation.

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 $3\text{:}26$ ($3$ minutes, $26$ seconds) for an athlete’s $800$m 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.

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

The range of possible times is $196.19$ seconds to $216.84$ seconds.
Which is $3\text{:}16.2$ to $3\text{:}36.8$.