# Adding two lines, what is the equation of the new line?

1. Apr 8, 2007

### saplingg

1. The problem statement, all variables and given/known data

Basically I was given a table displaying speed of a vehicle, thinking distance (distance it takes for driver to react) and braking distance. I am told to find an equation relating speed of vehicle and overall distance (overall distance = thinking distance + braking distance).

3. The attempt at a solution

Using graphing software, I've managed to find an approximate equation relating speed and thinking distance, as well as an equation relating speed and braking distance.

The equations are :

For speed vs thinking dist., y = (16/3)x, where y is speed of vehicle and x is thinking distance
and
For speed vs braking dist., y = 13(x^0.5), where y is the speed of vehicle and x is braking distance

Is there any way I can find an equation for speed versus overall distance using these 2 equations that I've obtained?

2. Apr 8, 2007

### Hurkyl

Staff Emeritus
Sure. It might be more obvious if you didn't use the same letter to denote thinking distance and braking distance.

(And shouldn't those constants have some units on them?)

3. Apr 8, 2007

### saplingg

Could anyone show me how?

@Hurkyl: I used subscripts to distinguish the distances

4. Apr 8, 2007

### HallsofIvy

Staff Emeritus
You are talking about the TOTAL distance aren't you?

(And you titled this "ADDING two lines"!)

5. Apr 8, 2007

### saplingg

yeah what is wrong with that?

6. Apr 8, 2007

### saplingg

Err It's ok, I've solved it. Thanks to all who read