SOLUTION: Hi. May I have some help with the following problem? For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the followin

Question 121556: Hi. May I have some help with the following problem?
For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the following formula, where d is measured in feet. Kerry wants her stopping distance not to exceed d = 400 ft. At what range of speeds can she travel?
d=v+(v^2)/20
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
400=V+(V^2)/20
400=(20V+V^2)/20 CROSS MULTIPLY
V^2+20V=20*400
V^2+20V=8000
V^2+20V-8000=0
(V+100)(V-80)=0
V-80=0
V=80 MPH OR LESS IS THE ANSWER.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First thing is to realize what 'not to exceed' means. More than 400 feet exceeds 400 feet, but exactly 400 feet or anything less does not. So you want to determine v such that

is the given model. This is a reasonably good model presuming you have a better than average reaction time, dry pavement, new tires, etc. Be that as it may, you need to determine v such that:

Multiply by 20

(Since you multiplied by a positive number, the sense of the inequality remains the same)

Add -8000 to both sides

Factor

So or Since we can exclude this root as redundant.

Check:

,
, and
.

Answer checks.

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