Julian Travels 200 miles averaging a certain speed. If the car had gone 10 mph faster the trip would have take 1 hour less. find Julian's average speed

Question

If a and b are the lengths of two legs of a right triangle and c is the length of the hypotenuse hen a^2+b^2=c^3

Julian Travels 200 miles averaging a certain speed. If the car had gone 10 mph faster the trip would have take 1 hour less. find Julian's average speed

Answer 1

Since distance=speed*time

 

We can set up two equations with the information that we are given. The first equation represents actual events and the second the hypothetical situation.

 

vt=200 

(v+10)(t-1)=200

 

Solving for t in the first equation gives us:

t=200/v

 

Substitute this into the second equation for t gives us:

 

(V+10)(200/v-1)=200

 

After multiplying and rearranging we get the quadratic:

 

V^2+10v-2000=0

 

By Completing the Square we get:

 

(V+5)^2=2025

 

Solving for v and rejecting the negative solution gives us an answer of:

 

V=45 mph