College Algebra (6th Edition)

Since the contestant has to win within the $20 \frac{+}{} 5$ minute time frame, he models it in the following manner: $$|x - 20| \leq 5$$ To solve this, we break it into its two components: $$x - 20 \leq 5$$ $$or$$ $$x-20 \geq -5$$ Solving each individually, we get the following: $$x \leq5 + 20$$ $$x \leq 25$$ $$or$$ $$x \geq -5 + 20$$ $$x\geq 15$$ which satisfies the condition that he win within the $15-25$ minute time frame.