SOLUTION: Time taken by a train to travel a distance of 225 km was reduced by 20 minutes when the average speed was increased by 20 km/hr. Find its original speed correct to the nearest i

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Question 816178: Time taken by a train to travel a distance of 225 km was reduced by 20 minutes when the
average speed was increased by 20 km/hr. Find its original speed correct to the nearest integer.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Original - modified time = 20 minutes
d=225
speed =x
modified speed = x+20
t=d/r
225/x-225/(x+20) = 1/3
multiply by x(x+20)
225(x+20)-225x=x(x+20)/3
225x+4500-225x=(x^2+20x)/3
4500*3= x^2+20x
x^2+20x-13500 =0

solve by quadratic formula
a= 1 , b= 20 , c= -13500

b^2-4ac= 400 + 54000
b^2-4ac= 54400
%09sqrt%28%0954400%09%29=%09233.24%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=( -20 + 233.24 )/ 2
x1= 106.62
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( -20 -233.24 ) / 2
x2= -126.62
Ignore negative value
speed 106.62 mph