3.5 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 truck 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.

3.5.1 Find the distance between Pretoria and Benoni. (6)

3.5.2 What was the speed of the car before it passed the truck? (9)

3.5.3 At what time did the car reach Pretoria?

Let’s solve the problem step by step.

### 3.5.1 Find the distance between Pretoria and Benoni.

We are given that the truck left Pretoria at 09:00 and traveled at a constant speed of 50 km/h. We also know that by the time it passed the car at 12:00, it had traveled \( \frac{3}{7} \) of the total journey.

Let \( D \) be the total distance between Pretoria and Benoni.

- From 09:00 to 12:00, the truck traveled for 3 hours at 50 km/h.
  
Thus, the distance the truck traveled in 3 hours is:
\[
\text{Distance covered by the truck} = 50 \times 3 = 150 \, \text{km}
\]

Since this distance is \( \frac{3}{7} \) of the total journey, we can set up the equation:
\[
\frac{3}{7} D = 150
\]

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

So, the total distance between Pretoria and Benoni is **350 km**.

### 3.5.2 What was the speed of the car before it passed the truck?

Let’s now determine the speed of the car before it passed the truck.

- The car left Benoni at 09:30 and passed the truck at 12:00.
- This means the car traveled for \( 12:00 - 09:30 = 2.5 \) hours before passing the truck.
- The distance covered by the car in this 2.5 hours is \( \frac{4}{7} \) of the total distance \( D \), since the truck covered \( \frac{3}{7} \) of the journey by the time they passed each other.

Thus, the car covered \( \frac{4}{7} \times 350 = 200 \, \text{km} \) in 2.5 hours.

Let \( v \) be the speed of the car before passing the truck. We can now set up the equation:
\[
v = \frac{200}{2.5} = 80 \, \text{km/h}
\]

So, the speed of the car before it passed the truck was **80 km/h**.

### 3.5.3 At what time did the car reach Pretoria?

After passing the truck, the speed of the car decreased by 5 km/h. Therefore, the new speed of the car after passing the truck was:
\[
80 - 5 = 75 \, \text{km/h}
\]

- The remaining distance for the car after passing the truck was \( \frac{3}{7} \times 350 = 150 \, \text{km} \).
- The time taken to cover this remaining distance at 75 km/h is:
\[
\text{Time} = \frac{150}{75} = 2 \, \text{hours}
\]

Since the car passed the truck at 12

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 truck 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. 3.5.1 Find the distance between Pretoria and Benoni. 3.5.2 What was the speed of the car before it passed the truck? 3.5.3 At what time did the car reach Pretoria?

Solve a real-world problem involving distance, speed, and time. Learn how to find the total distance between Pretoria and Benoni, determine the speed of the car before passing the truck, and calculate the time the car reached Pretoria. Key mathematical concepts include algebra and the distance-speed-time relationship. Suitable for Grades 9-12.

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