Need for speed

Let the initial speed of the car be $x$ . Therefore, time taken by car to cover a distance of $32$ km is $\frac{32}{x}$ .

Now, when speed is increased to $x+4$ , time taken is $\frac{32}{x+4}$ , which is $4$ hours less than the initial time.

Therefore the equation becomes $\frac{32}{x}-4=\frac{32}{x+4}$

$\implies 32(x+4)-4x(x+4)=32x$

$\implies x^2+4x-32=0$

$=(x+8)(x-4)=0$

$\implies x=-8$ or $x=4$

Since speed cannot be negative, therefore $x=\boxed{4}$ .