A car left Johannesburg at 14:00 for Polokwane at a speed of 64 km/h. A truck left

Johannesburg an hour later. The car and the trucktruck did not change the speeds

throughout. At 16:30, the car was 70 km ahead of the truck. Find the speed of the

truck.

To solve this problem, we'll need to determine the speed of the truck by using the information provided about the car's speed and the time difference between when the car and the truck left Johannesburg.

### Step-by-Step Solution:

1. **Determine the distance traveled by the car:**

   - The car left at 14:00 and by 16:30 (2.5 hours later), the car was 70 km ahead of the truck.
   - The car was traveling at 64 km/h.
   - Distance traveled by the car in 2.5 hours:  
     \[
     \text{Distance} = \text{Speed} \times \text{Time} = 64 \, \text{km/h} \times 2.5 \, \text{hours} = 160 \, \text{km}
     \]

2. **Determine the time the truck has been traveling by 16:30:**

   - The truck left at 15:00 (1 hour after the car), so by 16:30, the truck had been traveling for 1.5 hours.

3. **Let the speed of the truck be \( x \) km/h:**

   - The distance traveled by the truck in 1.5 hours:  
     \[
     \text{Distance} = x \, \text{km/h} \times 1.5 \, \text{hours} = 1.5x \, \text{km}
     \]

4. **Use the given condition that at 16:30, the car was 70 km ahead of the truck:**

   - The distance difference between the car and the truck is given as 70 km, so:
     \[
     \text{Distance by car} - \text{Distance by truck} = 70 \, \text{km}
     \]
     \[
     160 \, \text{km} - 1.5x \, \text{km} = 70 \, \text{km}
     \]

5. **Solve for \( x \):**

   \[
   160 - 1.5x = 70
   \]
   \[
   1.5x = 160 - 70
   \]
   \[
   1.5x = 90
   \]
   \[
   x = \frac{90}{1.5} = 60 \, \text{km/h}
   \]

### Answer:
The speed of the truck is **60 km/h**.

Would you like any further explanation or have any additional questions?

Here are some related questions you might find interesting:
1. What would be the new distance between the car and the truck after 3 hours?
2. How much sooner would the car reach Polokwane if the truck traveled at the same speed?
3. What if the truck had left Johannesburg at the same time as the car?
4. How would the solution change if the car traveled at 80 km/h instead of 64 km/h?
5. If the truck increased its speed by 10 km/h halfway through the journey, what would be the new distance between them?

**Tip:** When solving problems involving relative speed or distances, setting up equations based on the given information is crucial to finding the correct solution.

A car left Johannesburg at 14:00 for Polokwane at a speed of 64 km/h. A truck left Johannesburg an hour later. The car and the truck did not change their speeds throughout. At 16:30, the car was 70 km ahead of the truck. Find the speed of the truck.

Learn how to solve a problem involving the speed of a truck and a car traveling between Johannesburg and Polokwane. This step-by-step solution uses algebra and the distance formula to find the truck's speed based on the given conditions. Ideal for Grades 7-10.

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