Given,
The girl covers a distance of 6 km at a speed x km/hr.
So,, the time taken to cover first 6 km 6 km=6/x hrs. [Since, Time = Distance / Speed]
Also given, the girl covers the remaining 6 km distance at a speed (x+2) km/hr
So, the time taken to cover a next 6 km=6/(x+20)
And, the total time taken to cover the whole distance = 2 hrs 30 mins = (120+30)/60=5/2 hrs
Then the below equation can be formed,
∴6x+6x+2=52
6x+12+6xx(x+2)=52
12+12xx2+2x=52
24+24x=5x2+10x
5x2−14x−24=0
5x2−20x+6x−24=0
5x(x−4)+6(x−4)=0
(5x+6)(x−4)=0
x=−65,4
24+24x=5x2+10x
5x2−14x−24=0
5x2−20x+6x−24=0
5x(x−4)+6(x−4)=0
(5x+6)(x−4)=0
So, x=−6/5 or 4
As speed cannot be negative. x=4 is only valid.
Therefore, the value of x is 4.