SOLUTION: Over a distance of 240km, the average speed of a train is 20km/h faster than that of a car. It takes the car 30 minutes longer to cover the same distance. What is the speed of the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Over a distance of 240km, the average speed of a train is 20km/h faster than that of a car. It takes the car 30 minutes longer to cover the same distance. What is the speed of the       Log On


   

Question 536716: Over a distance of 240km, the average speed of a train is 20km/h faster than that of a car. It takes the car 30 minutes longer to cover the same distance. What is the speed of the car and the speed of the train?
Thank you for any help:)
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
speed of car = x
speed of train = x+20
d=240
t=d/r
time car - time train = 1/2 hour
(240/x)-240/(x+20)=1/2
LCD = x(x+20)
240(x+20)-240x= x(x+20)/2
240x+4800-240x=(x^2+20x)/2
9600=x^2+20x
x^2+20x-9600=0
Find the roots of the equation by quadratic formula

a= 1 ,b= 20 ,c= -9600

b^2-4ac= 400 + 38400
b^2-4ac= 38800
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=%28-12%2B21%29%2F%2812%29
x1=( -20 + 196.98 )/ 2
x1= 88.49 88 43/88
x2=( -20 -196.98 ) / 2
x2= -108.49
Ignore negative value
car speed = 88.49 mph