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, find `x`.

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Solution

The girl covers half of the distance at the speed of x km/h and the remaining at a speed of x+2 km/h.
so

$6 over x plus fraction numerator 6 over denominator x plus 2 end fraction equals 2.5 fraction numerator 12 x plus 12 over denominator x left parenthesis x plus 2 right parenthesis end fraction equals 2.5$

$\frac{24 x + 24}{x (x + 2)} = 5$

$24 x + 24 = 5 x^{2} + 10 x$

$5 x^{2} - 14 x - 24 = 0$

$(x - 4) (5 x + 6) = 0$

$x = 4, \frac{- 6}{5}$

the negative value is neglected

so

x = 4

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