Question

A man travels 108 km and finds that he could have made the journey in$4\frac{1}{2}$ hrs less, had he traveled 2 km per hr faster. At what rate did he travel?

Answer 1

Let the man travels with speed=x km/h

So time taken to cover the distance of$108km=\frac{108km}{x}$

If speed increases by 2km/h

Now, speed =x+2

Then time requires to cover, $108km=\frac{108km}{x+2}$

these two time has difference of , $4\frac{1}{2}=\frac{9}{2}h$

$\frac{108}{x}-\frac{108}{x+2}=\frac{9}{2}$

$\frac{108x(x+2)-108x}{x(x+2)}=\frac{9}{2}$

$\frac{108x^2+216-108x}{(x^2+2x)}=\frac{9}{2}$

$\frac{216}{x^2+2x}=\frac{9}{2}$

$9(x^2+2x)=216\times 2$

$9x^2+18x=432$

$9x^2+18x-432=0$

$x^2+2x-48=0$

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

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

Since, speed can not be negative, so $x=6km{h}^{-1}$