Answer: Roman will catch up Jordan after 0.5 h, and they will be 30 miles into the conmute.
Explanation:
1) Data:
Jordan's speed: r1 = 56 mi / h
Roman's speed: r2 = 60 mi / h
Jordan's initial position: 2 miles
Roman's initial position: 0 miles
2) Formula:
Both motions are at constant speed, so rate = distance / time
Position = Initial position + distance run = initial position + rate * time
3) Solution:
Jordan's position, x1 = 2 mi + 56 mi / h * t
Roman's position, x2 = 0 mi + 60 mi/h * t = 60 mi / h
They start driving at the same time, so their times are equal.
When Roman catch up Jordan their position are equal => x1 = x2
=> 2 + 56t = 60 t
=> 60t - 56t = 2
=> 4t = 2
=> t = 2/4 = 0.5 hours
Now you can calculate the position of both in the commute:
From Jordan's rate: x1 = 2 mi + 56 mi /h * 0.5 h = 2mi + 28mi = 30 mi
From Roman's rate: x2 = 60 mi/h * 0.5 h = 30 mi
Answer: Roman will catch up Jordan after 0.5 h, and they will be 30 miles into the conmute.
