A truck left Pretoria at 09:00 and travelled to Benoni at a speed of 50km/h throughout the whole journey. A car left Benoni at 09:30 and travelled to Pretoria. The speed of the car remained the same until it passed the lorry at 12:00. The truck has travelled 3 7 of the journey when it passed the car. The speed of the car decreased by 5km/h after it passed the truck and it travelled at this new speed for the rest of the journey. 2.5.1 Find the distance between Pretoria and Benoni. (6) 2.5.2 What was the speed of the car before it passed the truck? (9) 2.5.3 At what time did the car reach Pretoria?

### 2.5.1 **Finding the Distance Between Pretoria and Benoni**

Let the total distance between Pretoria and Benoni be denoted as \( D \) (in kilometers).

- The truck started its journey at 09:00, traveling at a speed of \( 50 \ \text{km/h} \).
- The truck passed the car at 12:00, which means it traveled for 3 hours (\( 12:00 - 09:00 = 3 \ \text{hours} \)).
  
In this 3-hour period, the truck traveled:
\[
\text{Distance traveled by the truck} = 50 \times 3 = 150 \ \text{km}
\]
It is also given that when the truck passed the car, it had traveled \( \frac{3}{7} \) of the total journey.

Thus:
\[
\frac{3}{7} \times D = 150
\]

Solving for \( D \):
\[
D = \frac{150 \times 7}{3} = 350 \ \text{km}
\]

**Answer:** The total distance between Pretoria and Benoni is \( 350 \ \text{km} \).

---

### 2.5.2 **Finding the Speed of the Car Before It Passed the Truck**

Let the speed of the car before passing the truck be denoted as \( v \ \text{km/h} \).

- The car left Benoni at 09:30 and passed the truck at 12:00, meaning the car traveled for \( 2.5 \ \text{hours} \) before passing the truck.
  
In this time, the car covered \( \frac{4}{7} \) of the total journey, since the truck had covered \( \frac{3}{7} \) of the journey and the car had to cover the remaining \( \frac{4}{7} \) of the distance to meet the truck.

The car’s distance covered is:
\[
\frac{4}{7} \times 350 = 200 \ \text{km}
\]

Thus, the speed of the car before passing the truck can be calculated as:
\[
v = \frac{200}{2.5} = 80 \ \text{km/h}
\]

**Answer:** The speed of the car before it passed the truck was \( 80 \ \text{km/h} \).

---

### 2.5.3 **Finding the Time the Car Reached Pretoria**

After passing the truck, the car reduced its speed by \( 5 \ \text{km/h} \), so its new speed is:
\[
v_{\text{new}} = 80 - 5 = 75 \ \text{km/h}
\]

The remaining distance for the car after passing the truck is:
\[
\frac{3}{7} \times 350 = 150 \ \text{km}
\]

Now, the time taken to travel this remaining distance at the reduced speed of \( 75 \ \text{km/h} \) is:
\[
\text{Time} = \frac{150}{75} = 2 \ \text{hours}
\]

Since the car passed the truck at 12:00, adding 2 hours means the car reached Pretoria at:
\[
12:00 + 2 = 14:00
\]

**Answer:** The car reached Pretoria at \( 14:00 \).

---

### Do you want more details on any part of this explanation or have any questions?

### Related Questions:
1. What would be the truck's total time for the entire journey from Pretoria to Benoni?
2. How much time did the car save by traveling faster before meeting the truck?
3. How far from Pretoria were both vehicles when they met?
4. If the car hadn't reduced its speed, when would it have reached Pretoria?
5. What would happen to the meeting time if the truck had been traveling at 60 km/h?

### Tip: 
When calculating time, always remember that time is the ratio of distance to speed. Keeping this in mind simplifies many motion problems.

A truck left Pretoria at 09:00 and travelled to Benoni at a speed of 50km/h throughout the whole journey. A car left Benoni at 09:30 and travelled to Pretoria. The speed of the car remained the same until it passed the lorry at 12:00. The truck has travelled 3/7 of the journey when it passed the car. The speed of the car decreased by 5km/h after it passed the truck and it travelled at this new speed for the rest of the journey. 2.5.1 Find the distance between Pretoria and Benoni. 2.5.2 What was the speed of the car before it passed the truck? 2.5.3 At what time did the car reach Pretoria?

Learn how to solve a motion problem involving a truck and a car traveling between Pretoria and Benoni. The problem covers key mathematical concepts like distance-speed-time relationships, proportions, and uniform motion. Suitable for Grades 10-12, this example involves calculating the distance between cities, the car's speed, and the arrival time in Pretoria.

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