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

## Homework Statement

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).

## 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?

Hurkyl
Staff Emeritus
Gold Member
Is there any way I can find an equation for speed versus overall distance using these 2 equations that I've obtained?
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?)

Could anyone show me how?

@Hurkyl: I used subscripts to distinguish the distances

HallsofIvy