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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

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60 mph................
User Tonimarie
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Answer: Roman will catch up Jordan after 0.5 h, and they will be 30 miles into the conmute.

Step-by-step 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.

User Shivansh Goel
by
8.9k points

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