For his exercise today, Jose plans to both run and swim. Let r be the number of laps he runs and let s be the number of laps he swims. Each lap he runs takes him 5 minutes, and each lap he swims takes him 3 minutes.

Question

He wants to exercise for more than 30 minutes today. Using the values and variables given, write an inequality describing this.

Answer 1

To express Jose's exercise plan as an inequality, we need to consider the time he spends running and swimming in relation to the total time he wants to exceed, which is 30 minutes.

1. Each lap he runs takes \(5\) minutes, so the total time spent running is \(5r\) minutes for \(r\) laps.
2. Each lap he swims takes \(3\) minutes, so the total time spent swimming is \(3s\) minutes for \(s\) laps.

Combining these, the total exercise time (in minutes) can be expressed as: \[ 5r + 3s \]

Since he wants to exercise for more than \(30\) minutes, we set up the inequality: \[ 5r + 3s > 30 \]

This inequality describes the condition for Jose's exercise plan.