The distance between two milestones is 230 km and two cars start simultaneously from the milestones in opposite directions. The distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/hr, then find the speed of each car.

Let's denote the speed of the slower car as \( x \) km/hr. Then the speed of the faster car would be \( x + 10 \) km/hr.

The two cars are moving towards each other, so their combined speed is the sum of their individual speeds:

\[
\text{Combined speed} = x + (x + 10) = 2x + 10 \text{ km/hr}
\]

In 3 hours, the distance covered by both cars together would be:

\[
\text{Distance covered in 3 hours} = \text{Combined speed} \times \text{Time} = (2x + 10) \times 3 \text{ km}
\]

Given that the distance between the cars after 3 hours is 20 km, the total distance covered by the two cars combined is:

\[
\text{Distance covered by both cars} = 230 \text{ km} - 20 \text{ km} = 210 \text{ km}
\]

So, we can set up the equation:

\[
(2x + 10) \times 3 = 210
\]

Let's solve for \( x \):

\[
6x + 30 = 210
\]

Subtract 30 from both sides:

\[
6x = 180
\]

Divide both sides by 6:

\[
x = 30 \text{ km/hr}
\]

Thus, the speed of the slower car is \( 30 \) km/hr, and the speed of the faster car is:

\[
x + 10 = 30 + 10 = 40 \text{ km/hr}
\]

### Final Answer:
- The speed of the slower car is **30 km/hr**.
- The speed of the faster car is **40 km/hr**.

Would you like to see the steps in more detail or have any other questions?

### Related Questions:

1. How would the problem change if the initial distance between the cars was 300 km?
2. What if the slower car's speed was reduced by 5 km/hr?
3. How does the time interval affect the final distance between the cars?
4. What if the speed difference between the cars was 15 km/hr?
5. How would the problem change if the cars started at the same milestone and traveled in the same direction?
6. How can you solve the problem if only the time difference between the cars' arrivals at the destination is given?
7. What if one car traveled for an additional hour compared to the other?
8. How would you set up an equation if the initial speeds of the cars were not constant?

**Tip:** When solving relative speed problems, clearly differentiate between scenarios where objects move towards each other versus when they move in the same direction.

Learn how to find the speeds of two cars moving towards each other problem with a detailed step-by-step solution. This problem involves calculating speeds based on relative motion and time, suitable for advanced high school students.

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