First 20 km at a speed of 17 km/h and second 20 km at a speed of 23 km/h ,what is the average speed of total journey?

To find the average speed of the total journey, we use the formula:

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

### Step 1: Calculate Total Distance
The total distance is the sum of the two distances traveled:

\[
\text{Total Distance} = 20 \text{ km} + 20 \text{ km} = 40 \text{ km}
\]

### Step 2: Calculate Time for Each Segment
1. **Time for the first 20 km at 17 km/h:**
   \[
   \text{Time}_1 = \frac{20 \text{ km}}{17 \text{ km/h}} = \frac{20}{17} \text{ hours}
   \]

2. **Time for the second 20 km at 23 km/h:**
   \[
   \text{Time}_2 = \frac{20 \text{ km}}{23 \text{ km/h}} = \frac{20}{23} \text{ hours}
   \]

### Step 3: Calculate Total Time
\[
\text{Total Time} = \frac{20}{17} + \frac{20}{23} \text{ hours}
\]

### Step 4: Calculate the Average Speed
\[
\text{Average Speed} = \frac{40 \text{ km}}{\frac{20}{17} + \frac{20}{23}} \text{ km/h}
\]

To simplify this expression, let's find the sum of the times:

\[
\frac{20}{17} + \frac{20}{23} = \frac{20 \times 23 + 20 \times 17}{17 \times 23} = \frac{460 + 340}{391} = \frac{800}{391} \text{ hours}
\]

So, the average speed is:

\[
\text{Average Speed} = \frac{40}{\frac{800}{391}} = \frac{40 \times 391}{800} = \frac{15640}{800} \approx 19.55 \text{ km/h}
\]

### Final Answer
The average speed of the total journey is approximately \( 19.55 \) km/h.

Would you like further details or have any questions?

### Related Questions
1. How do you calculate average speed for a journey with multiple segments?
2. What is the impact of varying speeds on total travel time?
3. How would the average speed change if the second segment speed was different?
4. Can we use the harmonic mean to find average speed directly in such cases?
5. What if the journey was split into more segments with different speeds?

**Tip:** When dealing with average speeds, remember that it's not simply the arithmetic mean of the speeds. It's crucial to consider the total distance and total time taken.

First 20 km at a speed of 17 km/h and second 20 km at a speed of 23 km/h, what is the average speed of total journey?

Find out how to calculate the average speed for a journey with two segments: 20 km at 17 km/h and 20 km at 23 km/h. This solution walks you through the key formulas and concepts of speed, distance, and time, providing a step-by-step guide for students in Grades 8-10.

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