Question

a man Travels 108 km and find he could have made the journey in 9 by 2 hours Less, had travelled 2 km an hour faster at what rate did he travel

Answer 1

let the man travels with speed x km/hr

so time taken to cover the distance of 108 km ,

= 108 / x

if speed increases by 2 km/hr
i.e. now speed = x+2

then time requires to cover 108 km ,

= 108/ x+2

these two time has difference of 9/2 hour

therefore , 108/x - 108/x+2 =9/2

[108(x+2) -108x ] / x(x+2) = 9/2

108x + 216 -108x / x^2+2x = 9/2

216 / x^2+2x = 9/2


9 ( x^2+2x ) = 216 ×2


9 x^2 + 18x = 432

9 x^2 + 18x - 432 = 0

x^2 + 2x - 48 = 0

x^2 + 8x -6x - 48 = 0

x ( x + 8) - 6 ( x + 8) = 0

(x + 8 ) (x - 6 ) =0

(x + 8 ) = 0 or (x - 6 ) =0

x = -8 or x = 6

speed never minus
therefore x = -8 not possible

so , x =6

Answer 2

Answer:

Step-by-step explanation:

let the man travels with speed x km/hr

so time taken to cover the distance of 108 km ,

= 108 / x

if speed increases by 2 km/hr

i.e. now speed = x+2

then time requires to cover 108 km ,

= 108/ x+2

these two time has difference of 9/2 hour

therefore , 108/x - 108/x+2 =9/2

[108(x+2) -108x ] / x(x+2) = 9/2

108x + 216 -108x / x^2+2x = 9/2

216 / x^2+2x = 9/2

9 ( x^2+2x ) = 216 ×2

9 x^2 + 18x = 432

9 x^2 + 18x - 432 = 0

x^2 + 2x - 48 = 0

x^2 + 8x -6x - 48 = 0

x ( x + 8) - 6 ( x + 8) = 0

(x + 8 ) (x - 6 ) =0

(x + 8 ) = 0 or (x - 6 ) =0

x = -8 or x = 6

speed never minus

therefore x = -8 not possible

so , x =6