Jordan and roman travel the same route to work. jordan leaves work one morning and drives at a rate, r, of 56 mph. roman leaves the house soon after, when jordan has already traveled 2 mo. roman drives at a rate of 60 mph. how long after jordan leaves home well roman catch up to her? how many miles into the commute will this occur

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

Roman will catch up Jordan after 0.5 h, and they will be 30 miles into the conmute.

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