SOLUTION: The time for the bus trip between 2 towns is 45 minutes shorter than the time for a train trip. If they are 350 km apart and the train speed is 15 km/h slower than the bus, find th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The time for the bus trip between 2 towns is 45 minutes shorter than the time for a train trip. If they are 350 km apart and the train speed is 15 km/h slower than the bus, find th      Log On


   

Question 775877: The time for the bus trip between 2 towns is 45 minutes shorter than the time for a train trip. If they are 350 km apart and the train speed is 15 km/h slower than the bus, find the speed of the bus in km/h.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let bus speed =x
bus time = 350/x
Train speed = x-15 km/h
train time= 350/(x-15)
Train takes longer
Train time - bus time = 3/4 hour
350%2F%28x-15%29-350%2Fx+=3%2F4
multiply the equation by 4x(x-15)
4x*350-4*350(x-15)=3x(x-15)
1400x-1400x+21000=3x^2-45x

Rearrange
3x^2-45x-21000=0
/3
x^2-15x-7000=0
Find the roots of the equation by quadratic formula

a= 1 , b= -15 , c= -7000

b^2-4ac= 225 + 28000
b^2-4ac= 28225
%09sqrt%28%0928225%09%29=%09168%09
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=( 15 + 168 )/ 2
x1= 91.50
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 15 -168 ) / 2
x2= -76.50
Ignore negative value
bus speed 91.50 km/h