The centers of 2 wheels are horizontally 31 cm apart. The diameter of the larger wheel is 14 cm and the diameter of the smaller wheel is 5 cm. Find the actual distance between the centers of the two wheels.

To solve this, we need to find the distance between the centers of the two wheels, accounting for their different sizes.

### Step 1: Understanding the problem
- The centers of the two wheels are horizontally 31 cm apart, which is the distance between the outer edges of the wheels' diameters when the wheels are placed side by side.
- The diameters of the wheels are given as:
  - Larger wheel: \(14 \, \text{cm}\)
  - Smaller wheel: \(5 \, \text{cm}\)

### Step 2: Calculate the distance between the centers
We know that the actual distance between the centers of the wheels is the 31 cm horizontal distance plus half of the diameters of both wheels.

1. **Half of the diameter of the larger wheel**:  
   \[
   \frac{14 \, \text{cm}}{2} = 7 \, \text{cm}
   \]
   
2. **Half of the diameter of the smaller wheel**:  
   \[
   \frac{5 \, \text{cm}}{2} = 2.5 \, \text{cm}
   \]

### Step 3: Add these values to the horizontal distance
The total distance between the centers of the two wheels is:
\[
31 \, \text{cm} + 7 \, \text{cm} + 2.5 \, \text{cm} = 40.5 \, \text{cm}
\]

### Final Answer:  
The actual distance between the centers of the two wheels is \( \boxed{40.5 \, \text{cm}} \).

Would you like further details or have any other questions?

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Here are 5 related questions to deepen your understanding:
1. What would the distance between the centers be if the larger wheel had a diameter of 20 cm?
2. How would the solution change if the horizontal distance was measured as 40 cm?
3. If both wheels had the same diameter of 10 cm, what would be the actual distance between their centers?
4. How do you calculate the total perimeter of the larger wheel if you are given the diameter?
5. How does the diameter of a circle relate to its radius?

**Tip**: The radius of a circle is always half of its diameter!

Learn how to calculate the actual distance between the centers of two wheels with diameters of 14 cm and 5 cm, given a horizontal separation of 31 cm. This problem explains step-by-step how to apply basic circle geometry and distance calculation, suitable for students in Grades 6-8.

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