Question

Ashish goes to his friends house which is 12 km away from his house. He covers half of the distance at a speed of x km per hour and the remaining at (x+2)km per hour. If he takes 2 hrs 30 min to cover the whole distance, find the value of 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

• Distance (s) = 12 km

• Time (t) = 2 hours 30 minutes

=> 2.5 hrs. = $\dfrac{5}{2}$

• Speed during 1st half = x km/hr.

• Speed during 2nd half = (x + 2) km/hr.

_____________ [ GIVEN ]

• We have to find the value of x. (distance)

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Now..

» Speed = $\dfrac{Distance}{Time}$

Time = $\dfrac{Distance}{Speed}$

a) Time taken for first half = $\dfrac{Distance}{Speed}$

=> Time = $\dfrac{6}{x}$ ________ (eq 1)

b) Time taken for second half = $\dfrac{Distance}{Speed}$

=> Time = $\dfrac{6}{x+2}$ ________ ( eq 2)

» Add (eq 1) & (eq 2)

=> $\dfrac{6}{x}$ + $\dfrac{6}{x+2}$ = $\dfrac{5}{2}$

=> $\dfrac{ 6x\: + \:12 \: + \: 6x }{ {x}^{2} \: + \: 2x }$ = $\dfrac{5}{2}$

=> $\dfrac{12 x\: + \: 12 }{ {x}^{2} \: + \: 2x }$ = $\dfrac{5}{2}$

Cross-multiply them

=> 2(12x + 12) = 5(x² + 2x)

=> 24x + 24 = 5x² + 10x

=> 5x² + 10x - 24x - 24 = 0

=> 5x² - 14x - 24 = 0

=> 5x² - 20x + 6x - 24 = 0

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

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

=> x = -6/5 (neglected because time can't be negative)

So..

=> x = 4

_____________________________

Distance = 4 km/hr.

_________ [ ANSWER ]

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