Jose drove 300 miles on his vacation. He drove an average of 1.5 times faster on the second 150 miles of his trop than he did on the first 150 miles of his trip. How much time did he spend driving? Let x = his speed on the first half of the trip.

Step-by-step explanation:

Given

Jose drives

In first 150 miles he 1.5 times faster than the second half

Let be the speed on the second half so

in first half speed is

time taken in first half

For second half

Total time

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0