Question

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

Answer 1

Answer:

x = 4

Step-by-step explanation:

Let the original speed be x (speed during 1st half)

Speed during 2nd half - x + 2

Time - 2h 30 min = 2.5 h = 5/2

Speed = distance / time

therefore , t = 6/x   and     t` = 6/x+2  

6/x + 6/x+2 = 5/2

6(x+2) + 6(x)/(x+2)(x) = 5/2

6x + 12 +6x/x2 +2x = 5/2

12x + 12/ x2 +2 x  = 5/2

2(12x + 12 ) = 5(x2 + 2x)

24x + 24 = 5x2 + 10x

24x - 10x = 5x2 - 24

14x = 5x2 - 24

5x2 - 14x - 24 = 0

5x2 - 20x + 6x - 24 = 0

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

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

5x+6 = 0

x = -  6/5

x - 4= 0

x = 4

speed can't be negative

therefore , x = 4