Question

write inequalities to represent the situations below.
to be eligible for the senior admission rate, a visitor must not be less than 60 years old.
use y to represent the age (in years) of a visitor who gets the senior rate.
to qualify for the championship, a runner must complete the race in at most 40 minutes.
use t to represent the time (in minutes) of a runner who qualifies for the championship.

Explanation:

Step1: Analyze the first situation

The problem states a visitor must not be less than 60 years old to get the senior rate. Let \( y \) be the age. "Not less than" means greater than or equal to. So the inequality is \( y \geq 60 \).

Step2: Analyze the second situation

A runner must complete the race in at most 40 minutes to qualify. Let \( t \) be the time. "At most" means less than or equal to. So the inequality is \( t \leq 40 \).

Answer:

For the senior admission rate: \( y \geq 60 \)
For the championship qualification: \( t \leq 40 \)