3. At an intersection, two cars collided. After some time, they both started moving again simultaneously. One headed north at a speed of $54 \mathrm{~km} / \mathrm{h}$, and the other headed west. After 20 minutes, they were $30 \mathrm{~km}$ apart. At what speed was the second car moving?
3. Let's denote the cars as A and B.

Sketch:

![](https://cdn.mathpix.com/cropped/2024_05_30_494875a1129ddb904645g-22.jpg?height=633&width=648&top_left_y=366&top_left_x=310)

From the problem statement, we observe that the movement of the cars can be sketched as a right-angled triangle.

1 POINT

![](https://cdn.mathpix.com/cropped/2024_05_30_494875a1129ddb904645g-22.jpg?height=322&width=488&top_left_y=1141&top_left_x=333)

If car A is moving at a speed of $54 \mathrm{~km} / \mathrm{h}$, after 20 minutes it will cover a distance of 18 kilometers.

In that time, car B will cover a distance of $24 \mathrm{~km}$, as according to the Pythagorean theorem,

$x=\sqrt{30^{2}-18^{2}}=\sqrt{576}=24$.

2 POINTS

If in twenty minutes a car covers a distance of $24 \mathrm{~km}$, in one hour it will cover three times the distance, i.e., 72 km. Therefore, its speed is $72 \mathrm{~km} / \mathrm{h}$.

1 POINT TOTAL 6 POINTS