SOLUTION: 1. Jake drives a tractor from one town to another, a distance of 120 kilometers. He drives 6 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast do

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1. Jake drives a tractor from one town to another, a distance of 120 kilometers. He drives 6 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast do      Log On


   

Question 715505: 1. Jake drives a tractor from one town to another, a distance of 120 kilometers. He drives 6 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast does he drive each way?
Going?, Returning?
2.The oriental rug shown is 3 feet longer than it is wide. If the diagonal of the rug is 12 feet find its dimensions to the nearest tenth of a foot.
width?, length?
3. A large rectangular movie screen in an IMAX theater has an area of 10,176 square feet. Find the dimensions of the screen if it is 10 feet longer than it is wide. Length?, Width?
4.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Tie going - time returning = 1 hours
let speed be x km/h
time = d/r
d=120
time going = 120/x
time returning = 120/(x+6)
120%2Fx+-+120%2F%28x%2B6%29+=+1
multiply the equation by x(x+1)
120(x+1) -120x= x(x+1)
120x+120-120x=x^2+x
x^2+x-120=0
Find the roots of the equation by quadratic formula

a= 1 b= 1 c= -120

b^2-4ac= 1 - -480
b^2-4ac= 481 sqrt%28%09481%09%29= 21.93
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -1 + 21.93 )/ 2
x1= 10.47
x2=( -1 -21.93 ) / 2
x2= -11.47
Ignore negative value km/h
x = 10.47 (going speed)
add 6 for returning speed


width =x
length = x+3
Area = L * W
Area = x(x+3) = 12
x^2+3x=12
x^2+3x-12=0
solve for x
(x+4)(x-3)=0
x= 3 which is positive
the dimensions are 4 ft by 3 ft