A car travels 50 km at 60 km/h and another 50 km at 40 km/h. What is its average speed for the entire journey?

To calculate the average speed for the entire journey, we need to use the formula for average speed, which is:

\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\]

### Step 1: Calculate the total distance
The car travels 50 km at 60 km/h and another 50 km at 40 km/h. The total distance is:

\[
\text{Total distance} = 50 \, \text{km} + 50 \, \text{km} = 100 \, \text{km}
\]

### Step 2: Calculate the time for each leg of the journey
To calculate the time for each leg, we use the formula:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

- For the first part of the journey (50 km at 60 km/h):
  \[
  \text{Time}_1 = \frac{50 \, \text{km}}{60 \, \text{km/h}} = \frac{5}{6} \, \text{hours}
  \]

- For the second part of the journey (50 km at 40 km/h):
  \[
  \text{Time}_2 = \frac{50 \, \text{km}}{40 \, \text{km/h}} = \frac{5}{4} \, \text{hours}
  \]

### Step 3: Calculate the total time
The total time is the sum of the two times:

\[
\text{Total time} = \frac{5}{6} \, \text{hours} + \frac{5}{4} \, \text{hours}
\]

To add these, first find a common denominator (which is 12):

\[
\frac{5}{6} = \frac{10}{12}, \quad \frac{5}{4} = \frac{15}{12}
\]

So:

\[
\text{Total time} = \frac{10}{12} + \frac{15}{12} = \frac{25}{12} \, \text{hours}
\]

### Step 4: Calculate the average speed
Now, we can calculate the average speed:

\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{100 \, \text{km}}{\frac{25}{12} \, \text{hours}} = 100 \times \frac{12}{25} = 48 \, \text{km/h}
\]

### Final Answer:
The average speed for the entire journey is **48 km/h**.

Would you like a more detailed explanation of any step or have any further questions?

Here are some related questions you might find interesting:
1. How does the average speed change if the car travels the same distances but at speeds of 80 km/h and 20 km/h?
2. How would the average speed differ if the car traveled 100 km at a constant speed instead of varying speeds?
3. What happens to the average speed if the car's speed during the second part of the journey is greater than its speed in the first part?
4. How can the formula for average speed be adapted if the distances of each segment of the journey are not equal?
5. How do you calculate the average speed for a journey involving multiple segments with different speeds and distances?

**Tip**: When calculating average speed over multiple segments, always consider the time spent on each segment, not just the distances traveled.

Learn how to calculate the average speed for a car that travels 50 km at 60 km/h and another 50 km at 40 km/h. This problem involves calculating total distance and total time, and applying the formula for average speed. Suitable for students in Grades 7-9.

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