https://file.aiquickdraw.com/mathbot/file/173030888035338948rt3.jpg

To solve this problem, let's determine the average speed for a round trip, where the speeds for each leg of the journey differ.

Given:
- Speed to the store = \( 20 \, \text{km/h} \)
- Speed returning from the store = \( 30 \, \text{km/h} \)

### Step-by-Step Solution:

1. **Define the Distance**:
   Let the one-way distance to the store be \( d \).

2. **Calculate the Time for Each Part of the Trip**:
   - **Time to the store**: \( t_1 = \frac{d}{20} \)
   - **Time back from the store**: \( t_2 = \frac{d}{30} \)

3. **Total Distance**:
   The total distance for the round trip is:
   \[
   \text{Total Distance} = d + d = 2d
   \]

4. **Total Time**:
   The total time for the round trip is:
   \[
   \text{Total Time} = t_1 + t_2 = \frac{d}{20} + \frac{d}{30}
   \]

   To add these, we find a common denominator:
   \[
   \text{Total Time} = \frac{3d}{60} + \frac{2d}{60} = \frac{5d}{60} = \frac{d}{12}
   \]

5. **Average Speed**:
   Average speed is given by:
   \[
   \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2d}{\frac{d}{12}} = 2d \times \frac{12}{d} = 24 \, \text{km/h}
   \]

### Answer:
The average speed for the round trip is \( \mathbf{24 \, \text{km/h}} \).

---

Would you like further details on the calculation steps?

---

### Related Questions:
1. What is the concept of harmonic mean, and how is it used in average speed problems?
2. How would the average speed change if the return speed was 40 km/h instead of 30 km/h?
3. Why is the average speed not simply the average of 20 km/h and 30 km/h?
4. How can we use the formula for average speed in physics and engineering problems?
5. What happens to the average speed if the distance each way is doubled?

### Tip:
For problems involving average speeds over equal distances with different speeds, consider using the harmonic mean rather than the arithmetic mean.

You drive to the store at 20 km/h and return by the same route at 30 km/h. Discounting the time spent at the store, what was your average speed?

Find the average speed for a round trip where the speeds are 20 km/h on the way to the store and 30 km/h on the return. Learn how to use harmonic mean in calculating average speeds over equal distances. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation