Jordan and Roman travel the same route to work. Jordan leaves for work one morning and drives at a rate, r, of 56 mph. Roman leaves the house soon after, when Jordan has already traveled 2 mi. Roman drives at a rate of 60 mph. How long after Jordan leaves home will Roman catch up to her? How many miles into their commute will this occur? Which system of equations models this problem?

Question

Mathematics

Smarty

14 March, 16:10

Jordan and Roman travel the same route to work. Jordan leaves for work one morning and drives at a rate, r, of 56 mph. Roman leaves the house soon after, when Jordan has already traveled 2 mi. Roman drives at a rate of 60 mph. How long after Jordan leaves home will Roman catch up to her? How many miles into their commute will this occur? Which system of equations models this problem?

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Answers (1)

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Cello · Answer 1

The system of equations:

d = 56 t + 2 (Jordan)

d = 60 t (Roman)

d - distance, t - time

56 t + 2 = 60 t

60 t - 56 t = 2

4 t = 2

t = 2 : 4

t = 0.5 h

d = 0.5 * 60 = 30 miles

Answer:

t = 30 minutes, d = 30 miles.