Question

Read the problem. 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?
A.d = 56t d = 58t
B. d = 56t d = 62t
C. d = 56t d = 60t – 2
D.d = 56t d = 60t + 2

Answer 1

Answer:

Option C is correct answer.

Step-by-step explanation:

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.

Equation for Jordan becomes:

$d=56t+2$  

Equation for Roman becomes:

$d=60t$  

We can solve this further,

$56t+2=60t$

$60t-56t=2$

t = 0.5 hours

And d = 0.5\times60 = 30 miles

Option C is correct answer.

Answer 2

Speed of Jordan while driving from his home  = 56 mph

After Jordan travels 2 miles then Roman started from his house.

Speed of Roman while driving after leaving home= 60 mph

Let after t hours they meet.

And let they  cover the distance =d i.e point at which meet.

  After time t distance covered by Jordan= 56 t +2

Roman has to cover the distance to catch Jordan= 60 t

       A.T.Q

⇒ 60 t=56 t + 2

⇒4 t=2

⇒t=1/2

So, when d = 56×1/2+2=28+2=30 miles

Roman will catch Jordan.

From the above four solutions ,( C.) d = 56 t ,d = 60 t – 2 , Satisfies the above criteria.

So  C is the correct answer.