Question

1. you jog at a rate of 6 miles per hour. your friend is 55 feet ahead of you and jogs at a rate of 6.6 feet per second. write and solve an inequality that represents the amounts of time that your friend is ahead of you.

Explanation:

Step1: Convert your speed to ft/s

First, convert 6 miles per hour to feet per second. We know that 1 mile = 5280 feet and 1 hour = 3600 seconds. So, the conversion is:
\( 6 \, \text{miles/hour} = 6 \times \frac{5280 \, \text{feet}}{3600 \, \text{seconds}} = 8.8 \, \text{feet/second} \).

Step2: Define variables and set up inequality

Let \( t \) be the time in seconds. Your distance covered in \( t \) seconds is \( 8.8t \) feet, and your friend’s distance covered in \( t \) seconds is \( 6.6t \) feet. Since your friend starts 55 feet ahead, the friend is ahead when:
\( 6.6t + 55 > 8.8t \).

Step3: Solve the inequality

Subtract \( 6.6t \) from both sides:
\( 55 > 2.2t \).

Divide both sides by 2.2:
\( t < \frac{55}{2.2} = 25 \).

Answer:

The inequality is \( 6.6t + 55 > 8.8t \), and the solution is \( t < 25 \) seconds (meaning your friend is ahead for less than 25 seconds).