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To solve this problem, we need to determine the time it will take for two cars moving towards each other from a distance of 490 kilometers to be 40 kilometers apart.

Let's define the variables:
- Distance between the cars initially: \( d = 490 \) kilometers
- Speed of the first car: \( v_1 = 70 \) km/h
- Speed of the second car: \( v_2 = 80 \) km/h
- Final distance between the cars: \( d_f = 40 \) kilometers

The total distance the two cars need to close is:
\[ \Delta d = d - d_f = 490 - 40 = 450 \text{ kilometers} \]

The combined speed of the two cars is:
\[ v_{\text{total}} = v_1 + v_2 = 70 + 80 = 150 \text{ km/h} \]

We need to find the time \( t \) it takes for the cars to close the distance \( \Delta d \):
\[ t = \frac{\Delta d}{v_{\text{total}}} = \frac{450 \text{ km}}{150 \text{ km/h}} = 3 \text{ hours} \]

Therefore, the time it will take for the two cars to be 40 kilometers apart for the first time is **3 hours**.

Do you want details or have any questions? 

Here are 5 related questions for further practice:

1. If the first car's speed was increased to 90 km/h while the second car's speed remained at 80 km/h, how long would it take for them to be 40 kilometers apart?
2. What would be the time taken if the initial distance between the two cars was 600 kilometers instead of 490 kilometers, with the same speeds?
3. If both cars were moving in the same direction with their respective speeds, how long would it take for them to be 40 kilometers apart?
4. If the initial distance between the cars was 490 kilometers and they started moving away from each other with the given speeds, how long would it take for them to be 600 kilometers apart?
5. How would the solution change if instead of traveling at constant speeds, each car accelerated at a rate of 5 km/h²?

**Tip:** When solving relative motion problems, always consider the combined speed if objects are moving towards each other or the relative speed if they are moving in the same or opposite directions.

Two cars are 490 kilometers apart when they start moving toward each other. If one travels 70 km/hr and the other travels 80 km/hr, how much time will pass before they are 40 kilometers apart for the first time?

Solve a relative motion problem involving two cars moving towards each other. The cars start 490 kilometers apart with speeds of 70 km/h and 80 km/h. Find the time it takes for them to be 40 kilometers apart. This problem involves relative speed calculations and basic linear equations, suitable for students in Grades 7-9.

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