If one car starts 30min sooner and goes the velocity of 5km/h, when will the second car catch up if it’s going 11km/h?

Let's break this problem down:

### Variables:
- **First car** speed: \( 5 \, \text{km/h} \)
- **Second car** speed: \( 11 \, \text{km/h} \)
- Time difference (head start): \( 30 \, \text{minutes} = 0.5 \, \text{hours} \)

### Step-by-step solution:

1. **Distance covered by the first car in 30 minutes (0.5 hours):**
   \[
   \text{Distance} = \text{Speed} \times \text{Time} = 5 \, \text{km/h} \times 0.5 \, \text{hours} = 2.5 \, \text{km}
   \]

   So, the first car has a 2.5 km head start.

2. **Relative speed of the second car compared to the first car:**
   \[
   \text{Relative speed} = 11 \, \text{km/h} - 5 \, \text{km/h} = 6 \, \text{km/h}
   \]

   This is the speed at which the second car is catching up to the first car.

3. **Time for the second car to catch up:**
   \[
   \text{Time to catch up} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{2.5 \, \text{km}}{6 \, \text{km/h}} = 0.4167 \, \text{hours}
   \]

   Converting hours to minutes:
   \[
   0.4167 \, \text{hours} \times 60 \, \text{minutes/hour} = 25 \, \text{minutes}
   \]

### Answer:
The second car will catch up to the first car in **25 minutes**.

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Would you like more details on any part of this solution?

Here are some related questions you could explore:
1. How far will both cars have traveled by the time they meet?
2. What if the first car had a head start of 1 hour?
3. How long would it take if both cars traveled the same speed?
4. What if the second car started 10 minutes later than expected?
5. How would the catch-up time change if the second car had a speed of 15 km/h?

**Tip:** When calculating relative motion, always subtract the velocities to find the effective speed at which one object is catching up to the other.

Find out how long it will take for a second car traveling at 11 km/h to catch up to a first car with a 30-minute head start traveling at 5 km/h. This problem covers concepts of relative speed, distance, and time, and is suitable for students in Grades 6-8.

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