# Position at Which 2 Cars Pass Each Other

1. May 29, 2015

### Staff: Mentor

1. The problem statement, all variables and given/known data
Anna is driving from Champaign to Indianapolis on I-74. She passes the Prospect Ave. exit at noon and maintains a constant speed of 75 mph for the entire trip. Chuck is driving in the opposite direction. He passes the Brownsburg, IN exit at 12:30pm and maintains a constant speed of 65 mph all the way to Champaign. Assume that the Brownsburg and Prospect exits are 105 miles apart, and that the road is straight.

How far from the Prospect Ave. exit do Anna and Chuck pass each other? x =

2. Relevant equations

Position equation: X(t)=X0 + VxT

3. The attempt at a solution

I've tried to solve this by graphing the position of both people on a graph and finding the point where the lines intersect. (Time on X-Axis in Hours, Position on Y-Axis in Miles, Origin centered at Prospect Ave.)

Using the position equation I set Anna's initial time and position as zero. Her velocity is 75 mph so the equation for her line is: Y=75X + 0, or just Y=75X
(The problem calls the vertical axis X in this case, but I've labeled it as Y instead since it's more familiar to everyone)

I think I'm having trouble with Chuck's equation though. Since he passes the Brownsburg exit 30 minutes after Anna passes the Prospect Ave. exit, I have to shift his line over by half an hour. I thought the equation was: (-65X-0.5) + 105
Velocity is 65 mph in the negative direction, and the -0.5 shifts his line over to the right to account for the fact that he passed Brownsburg 1/2 hour after Anna passed the Prospect Ave. exit.
However, graphing both of these lines and finding the intersection point of (0.75,55.98) is apparently not correct.

Not sure what I've done wrong here.

2. May 29, 2015

### Staff: Mentor

Found the problem. Chuck's equation should be Y=-65(X-0.5)+105, not Y=(-65X-0.5)+105.

3. May 29, 2015

### SammyS

Staff Emeritus
Your error can be traced back to "order of operations" .

If Chuck's distance from Prospect Ave. is given by y = (-65X-0.5) + 105, then what does that give for Chuck's distance from Prospect Ave. at time, x = 1/2 hour? It doesn't give y = 105, does it?

Added in Edit: I see you've found the problem.

4. May 29, 2015

### Staff: Mentor

Not when you screw up on where to place the parentheses!