Jaime is at a library that is 5 miles from her house. Her brother, Max, is at a rec center that is 4.5 miles from the house. The library and rec center both close at 6:00 p. m. Jaime and Max are beginning their training for soccer, so
they decide to run home. Jaime maintains a constant rate of 8 miles per hour, while Max runs at a constant rate of
7.5 miles per hour.
Which system of equations correctly represents these situations where d is the distance from home in miles and t is
the length of time in hours?

Option A is correct.

Step-by-step explanation:

Given:

Distance between house and Jaime's library = 5 miles

Speed of Jaime when he is running from library to house = 8 miles per hour

Distance between house and Max's rec center = 5 miles

Speed of Max when he is running from rec center to house = 7.5 miles per hour

let d be the distance between house and their position at t hours.

According to the Question,

Distance Jaime covered in t hour = 8t

Distance left = 5 - 8t

So, d = 5 - 8t    ⇒ d = -8t + 5

Distance Max cover in t hour = 7.5t

Distance left to cover = 4.5 - 7.5t    

So, d = 4.5 - 7.5 t  ⇒ d = 7.5t + 4.5

Therefore, Option A is correct.