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

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SUMMARY

The discussion focuses on deriving an equation for overall distance based on speed, thinking distance, and braking distance. The participant successfully identified two separate equations: y = (16/3)x for speed versus thinking distance and y = 13(x^0.5) for speed versus braking distance. The challenge was to combine these equations to express speed in relation to overall distance, which was ultimately resolved. The conversation highlights the importance of clarity in variable representation and the necessity of including units for constants.

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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?
 
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saplingg said:
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
 
You are talking about the TOTAL distance aren't you?

(And you titled this "ADDING two lines"!)
 
yeah what is wrong with that?
 
Err It's ok, I've solved it. Thanks to all who read
 

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