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.
1. Find the distance between pretoria and benoni

Let \( d \) represent the distance between Pretoria and Benoni in kilometers.

### Step 1: Find how far the truck traveled by 12:00

- The truck left Pretoria at 09:00 and traveled at a constant speed of 50 km/h.
- From 09:00 to 12:00, the truck has been traveling for 3 hours.
- In 3 hours, the truck would have traveled a distance of:
  \[
  \text{Distance traveled by truck by 12:00} = 50 \, \text{km/h} \times 3 \, \text{hours} = 150 \, \text{km}.
  \]
  
At the moment the truck passed the car at 12:00, it had traveled \( \frac{3}{7} \) of the total distance \( d \). Thus, we can set up the equation:
\[
\frac{3}{7}d = 150.
\]

### Step 2: Solve for the total distance \( d \)
To find the total distance \( d \), we solve:
\[
d = \frac{150 \times 7}{3} = 350 \, \text{km}.
\]

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

Would you like details on further steps regarding the car's speed change or more information about the journey?

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### Related Questions:
1. What was the speed of the car before passing the truck at 12:00?
2. How long did it take the car to meet the truck, and at what speed was it traveling?
3. What distance did the car cover after passing the truck, considering its reduced speed?
4. How long did it take the truck to complete the entire journey from Pretoria to Benoni?
5. What was the car's average speed for the entire journey?

### Tip:
Always track time intervals carefully in motion problems to determine when different vehicles or objects meet.

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. 1. Find the distance between Pretoria and Benoni.

This problem involves determining the distance between Pretoria and Benoni using constant speed and time. The truck travels at 50 km/h, and the car's speed changes after meeting the truck. This problem covers key algebraic concepts related to rates, proportions, and linear equations. Suitable for students in Grades 9-12.

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