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Let's analyze the problem step by step:

We have:
- Car A traveling at 20 meters per second.
- Car B traveling at 15 meters per second.
- Car A starts 200 meters behind Car B.

### Relative Speed:
The difference in speeds between the two cars is:

\[
\text{Relative speed} = 20 \, \text{m/s} - 15 \, \text{m/s} = 5 \, \text{m/s}
\]

### Time to Catch Up:
Since Car A is 200 meters behind Car B, we can calculate the time it will take for Car A to close this gap using the relative speed. The time \( t \) can be found using the formula:

\[
t = \frac{\text{Distance}}{\text{Relative speed}} = \frac{200 \, \text{m}}{5 \, \text{m/s}} = 40 \, \text{seconds}
\]

### Distance Traveled by Car A:
Now, to find out how far Car A must travel to catch up with Car B, we multiply the time by Car A's speed:

\[
\text{Distance traveled by Car A} = \text{Speed of Car A} \times \text{Time} = 20 \, \text{m/s} \times 40 \, \text{seconds} = 800 \, \text{meters}
\]

Therefore, Car A must travel **800 meters** before it catches up with Car B.

The correct answer is \( \boxed{800 \, \text{m}} \).

Would you like further explanation or have any questions? 

Here are 5 questions related to this problem:
1. How would the answer change if Car A were only 100 meters behind?
2. What if both cars were moving at the same speed?
3. How much time would Car A take to catch up if it moved at 25 meters per second instead?
4. Can you find the time at which Car B would cover 800 meters at its speed?
5. How would you adjust the formula if Car B was accelerating instead of moving at a constant speed?

**Tip:** When two objects are moving at constant speeds, using the concept of relative velocity simplifies the problem.

Car A, moving in a straight line at a constant speed of 20 meters per second, is initially 200 meters behind car B, moving in the same straight line at a constant speed of 15 meters per second. How far must car A travel from this initial position before it catches up with car B?

Solve the problem of Car A catching up to Car B using concepts of relative speed, time, and distance. In this problem, Car A moves at 20 meters per second and Car B at 15 meters per second, with an initial gap of 200 meters. Learn how to calculate the distance Car A must travel to catch up.

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