A cyclist travels 20 kilometers in 1 hour and 40 kilometers in 2 hours. What is the cyclist's average speed for the entire trip?

To find the cyclist's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken.

### Step 1: Calculate total distance
The cyclist travels:
- 20 kilometers in the first leg,
- 40 kilometers in the second leg.

Thus, the total distance traveled is:
\[
\text{Total Distance} = 20 \, \text{km} + 40 \, \text{km} = 60 \, \text{km}
\]

### Step 2: Calculate total time
The cyclist spends:
- 1 hour in the first leg,
- 2 hours in the second leg.

Thus, the total time taken is:
\[
\text{Total Time} = 1 \, \text{hr} + 2 \, \text{hrs} = 3 \, \text{hrs}
\]

### Step 3: Calculate average speed
The average speed \( \text{v}_{\text{avg}} \) is given by the formula:
\[
\text{v}_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}}
\]

Substitute the values:
\[
\text{v}_{\text{avg}} = \frac{60 \, \text{km}}{3 \, \text{hrs}} = 20 \, \text{km/hr}
\]

### Conclusion:
The cyclist's average speed for the entire trip is **20 km/h**.

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Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What would the cyclist's average speed be if the first leg took 2 hours instead of 1 hour?
2. How would the average speed change if the cyclist covered 60 kilometers in 3.5 hours?
3. What is the difference between instantaneous speed and average speed?
4. How can the average speed be affected by varying terrain or wind resistance?
5. If the cyclist had taken 4 hours for the entire trip, what would the average speed be?

**Tip:** To calculate average speed over multiple legs of a journey, always use the total distance and total time—not the average of individual speeds!

A cyclist travels 20 kilometers in 1 hour and 40 kilometers in 2 hours. What is the cyclist's average speed for the entire trip?

Find the average speed of a cyclist who travels 20 kilometers in 1 hour and 40 kilometers in 2 hours. This problem involves key concepts such as distance, time, and speed calculations, and is ideal for students in Grades 6-8.

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