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Question

A girl goes to her friend's house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x+2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, fins x.

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Solution

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
5x214x24=0
5x220x+6x24=0
5x(x4)+6(x4)=0
(5x+6)(x4)=0
x=65,4
24+24x=5x2+10x
5x214x24=0
5x220x+6x24=0
5x(x4)+6(x4)=0
(5x+6)(x4)=0
So, x=6/5 or 4
As speed cannot be negative. x=4 is only valid.
Therefore, the value of x is 4.

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