Question 567816
let speed be x km/h

increase by 15
=x+15

original time - time with increased speed = 1/2 hour

d=90 km

d/r = t

90/x-(90/(x+15)=1/2

multiply the equation by 2x(x+15) to eliminate the denominator
180(x+15)-180x=x(x+15)

180x+2700-180x=x^2+15x

90x cancels off

x^2+15x-2700=0

x^2+60x-45x-2700=0

x(x+60)-45(x+60)=0

(x+60)(x-45)=0

x= 45 km/h the original speed. Ignore negative value