A loaded truck travels at 60 km/h to the landfill, 240 km away.
 
When the truck is empty, it travels back at 80 km/h.
What is the overall average speed of the truck? 
(requires 2 decimal places)

To determine the overall average speed of the truck, we can use the formula for average speed when there are different speeds over the same distance:

\[
\text{Average Speed} = \frac{2 \times \text{Speed}_1 \times \text{Speed}_2}{\text{Speed}_1 + \text{Speed}_2}
\]

Where:
- \(\text{Speed}_1 = 60 \, \text{km/h}\) (the speed to the landfill),
- \(\text{Speed}_2 = 80 \, \text{km/h}\) (the speed back).

Now, let's calculate the overall average speed:

\[
\text{Average Speed} = \frac{2 \times 60 \times 80}{60 + 80} = \frac{9600}{140} = 68.57 \, \text{km/h}
\]

Thus, the overall average speed of the truck is **68.57 km/h**.

Would you like further explanation or have any questions?

Here are 5 related questions:
1. How would the average speed change if the speeds were different?
2. What is the total time taken for the round trip?
3. How is the concept of harmonic mean related to this problem?
4. What would happen to the average speed if both speeds were the same?
5. How do different distances affect the calculation of average speed?

**Tip:** When calculating average speed for round trips with different speeds, remember that it is not simply the arithmetic mean, but the harmonic mean that applies.

A loaded truck travels at 60 km/h to the landfill, 240 km away. When the truck is empty, it travels back at 80 km/h. What is the overall average speed of the truck? (requires 2 decimal places)

Find the overall average speed of a truck traveling to a landfill at 60 km/h and returning at 80 km/h, with a step-by-step calculation using the harmonic mean. Suitable for Grades 9-11 students, this problem teaches essential concepts in speed and motion.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation