SOLUTION: a trip between two towns in montana takes 4 hours under ideal conditions. The first 150 miles of the trip is on a interstate, and the second 130 miles is on a highway with a speed

Algebra ->  Rational-functions -> SOLUTION: a trip between two towns in montana takes 4 hours under ideal conditions. The first 150 miles of the trip is on a interstate, and the second 130 miles is on a highway with a speed      Log On


   

Question 65379This question is from textbook
: a trip between two towns in montana takes 4 hours under ideal conditions. The first 150 miles of the trip is on a interstate, and the second 130 miles is on a highway with a speed limit that is 10 miles per hour less than on interstate
a)if x represents the speed limit on the interstate, write an expression that represents the time spend at that speed
b) write an expression for the time spent on the other highway
c)write and solve an equation to find the speed limit on the interstate and on the highway This question is from textbook

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
150/X+130/(X-10)=4
[150(X-10)+130X]/X(X-10)=4
(150X-1500+130X]/(X^2-10X)=4
280X-1500=4X^2-40X=0
4X^2-40X-280X+1500=0
4X^2-320X+1500=0 USING THE QUADRATIC EQUATION X=(-B+-SQRTB^2-4AC])/2A WE GET
X=(320+-SQRT[-320*-320]-[4*4+1500])/2*4
X=(320+-SQRT[102400-24000])/8
X=(320+-SQRT[78400])/8
X=(320+-280)/8
X=(320+280)/8
X=600/8
X=75 MPH SOLUTION FOR THE INTERSTATE SPEED. 75-10=65 MPH FOR THE HIGHWAY.
PROOF
150/75+130/65=4
2+2=4
4=4
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