The front wheels of a wagon are `2pi` m in circumference and the back wheels are `3pi` m in circumference. When the front wheels have made 10 more revolutions than the back wheels, how many metres has the wagon travelled?

Answer

To solve the problem, we need to find out how far the wagon has traveled when the front wheels have made 10 more revolutions than the back wheels.

### Step-by-Step Solution:

1. **Identify the Circumference of the Wheels:**
- The circumference of the front wheels = \(2\pi\) m
- The circumference of the back wheels = \(3\pi\) m

2. **Let the Number of Revolutions of the Back Wheels be \(x\):**
- Since the front wheels have made 10 more revolutions than the back wheels, the number of revolutions of the front wheels = \(x + 10\).

3. **Calculate the Distance Travelled by Each Set of Wheels:**
- Distance travelled by the back wheels = Circumference × Number of Revolutions
\[ \text{Distance by back wheels} = 3\pi \times x \]
- Distance travelled by the front wheels = Circumference × Number of Revolutions
\[ \text{Distance by front wheels} = 2\pi \times (x + 10) \]

4. **Set the Distances Equal:**
- Since the wagon travels the same distance regardless of which wheels are considered, we can set the distances equal to each other:
\[ 3\pi x = 2\pi (x + 10) \]

5. **Simplify the Equation:**
- Distributing \(2\pi\) on the right side:
\[ 3\pi x = 2\pi x + 20\pi \]
- Rearranging the equation:
\[ 3\pi x - 2\pi x = 20\pi \]
\[ \pi x = 20\pi \]

6. **Solve for \(x\):**
- Dividing both sides by \(\pi\):
\[ x = 20 \]
- This means the back wheels have made 20 revolutions.

7. **Calculate the Distance Travelled by the Wagon:**
- Using the number of revolutions of the back wheels to find the distance:
\[ \text{Distance} = 3\pi \times 20 = 60\pi \text{ meters} \]

### Final Answer:
The wagon has travelled \(60\pi\) meters.