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We are given that two cars, **A** and **B**, are initially 400 meters apart. Car **A** is traveling east at 30 meters per second, and car **B** is traveling west at 20 meters per second. Both cars are on a collision course.

### To solve for the time before they collide:
1. **Relative speed**: Since both cars are moving towards each other, the relative speed is the sum of their speeds:
   \[
   v_{\text{relative}} = 30 \, \text{m/s} + 20 \, \text{m/s} = 50 \, \text{m/s}
   \]

2. **Time to collision**: The total distance between the two cars is 400 meters. The time it will take for them to collide can be found using the formula:
   \[
   t = \frac{\text{distance}}{\text{relative speed}} = \frac{400 \, \text{m}}{50 \, \text{m/s}} = 8 \, \text{seconds}
   \]

Thus, the two cars will collide after **8 seconds**.

### The correct answer is (1) 8.0 s.

Would you like further clarification on any part of the solution? Here are 5 related questions you might want to explore:

1. How does relative speed affect collision time in different directions?
2. What would happen if both cars were moving at the same speed?
3. How would the situation change if one car were stationary?
4. Can this problem be solved using a graphical approach?
5. How do we modify the formula if the cars accelerate towards each other?

**Tip**: For any two objects moving directly towards each other, the relative speed is simply the sum of their individual speeds.

Two cars, A and B, are 400 meters apart. Car A travels due east at 30 meters per second on a collision course with car B, which travels due west at 20 meters per second. How much time elapses before the two cars collide?

Explore the kinematics problem where two cars, A and B, are 400 meters apart and travel towards each other at speeds of 30 m/s and 20 m/s, respectively. Learn how to calculate the collision time using relative speed. Suitable for Grades 9-11.

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