Question

a girl goes to her friends house which is at a distance of 12 km . she cover half of distance at xkm/hr and the remaining distance at a speed of x+2km/hr .if she takes 2-hrs 30 minutes to cover the whole distance find x

Answer 1

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/x +6/x+6 = 2.5
12 + 12x / x(x+6) = 5/2
5x²- 14x - 24 = 0
x = 4, -6/5
negative value is neglected
so
x = 4

Answer 2

Hey friend, Harish here.

Here is your answer.

Given that,

$Distance = 12\ km$

$Time \ taken = 2 \ hrs 30 \mins$
 
                $= 2.5 \ hrs$

$speed \ during \ first\ half \distance = x \ km/hr$

$speed \ during \ second \ half \distance = x+2 \ km/hr$

We know that, 

$speed = \frac{distance}{time}$

$So, \ time = \frac{distance}{speed}$

i)$Time \ taken \ for \ first\ half = \frac{half \ distance}{speed}$

                                              $= \frac{6}{x}$   - (i)


ii)$Time \ taken \ for \ second\ half = \frac{half \ distance}{speed}$ 
 
                                                     $= \frac{6}{x+2}$

Now, add (i) & (ii). 

We get,

 $\frac{6}{x} + \frac{6}{x+2} = 2.5 hrs$

$6( \frac{x+2+x}{ x^{2} +2x}) = 2.5$

$12x+12 = (2.5) (x^{2}+2x)$

$2.5 x^{2} +5x -12x -12 = 0$

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

$5 x^{2} -20x +6x -24 = 0$

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

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

Therefore ,    x = 4 or x = -6/5

As speed "x" cannot be negative. X = 4 Km/hr.
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