3. From two points $A$ and $B$, the distance between which is 300 km, two cars set off simultaneously. The speed of the car that set off from $A$ is 40 km/h. Determine the speed of the second car, given that after two hours the distance between the cars was 100 km.
3. Since the problem does not specify the direction they were traveling, we need to consider two cases: moving in the same direction and moving in different directions.

First case. Moving in the same direction. Let the first car travel from $A$ to $B$ at a speed of 40 km/h.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-086.jpg?height=260&width=942&top_left_y=1840&top_left_x=563)

1) $40 \times 2=80$ (km) - the first car traveled in two hours $(A C)$
2) $300-80=220$ (km) - the remaining distance for the first car to reach $B(C B)$.

Since the second car was not moving towards the first, in this case, there cannot be a distance of 100 km between the first and second car after 2 hours, and the problem has no solution in this case.

Now let the first car travel from $A$ in the direction opposite to $B$.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-087.jpg?height=254&width=1050&top_left_y=518&top_left_x=503)

1) $40 \times 2=80$ (km) - the first car traveled in two hours $(A C)$
2) $100-80=20$ (km) - the remaining distance for the second car to reach $A$;
3) $300-20=280$ (km) - the distance the second car traveled in 2 hours;
4) $280: 2=140(\kappa m / h)$ - the speed of the second car.

Second case. The cars are moving in different directions. In this case, they can move in opposite directions or towards each other. In the first situation, it is obvious that there is no solution. Let's consider the second situation.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-087.jpg?height=254&width=945&top_left_y=1341&top_left_x=561)

1) $40 \times 2=80$ (km) - the first car traveled in two hours;
2) $300-100-80=120$ (km) — the distance the second car traveled in two hours;
3) $120: 2=60(\mathrm{km} / \mathrm{h})$ - the speed of the second car.

Answer: depending on the direction of movement, the speed of the second car is 60 km/h or 140 km/h.