The diameter of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at `24(6)/(11)` revolutions per minute. Find :
the distance travelled by the tractor in 40 minutes.

Answer

To solve the problem, we will follow these steps:

### Step 1: Convert the diameters to the same unit
The diameter of the front wheel is given as 63 cm, and the diameter of the rear wheel is given as 1.54 m. We need to convert the diameter of the rear wheel into centimeters.

1. **Conversion**:
\[ 1.54 \, \text{m} = 1.54 \times 100 \, \text{cm} = 154 \, \text{cm} \]

### Step 2: Calculate the radius of both wheels
The radius is half of the diameter.

1. **Front Wheel Radius**:
\[ R_{\text{front}} = \frac{63}{2} = 31.5 \, \text{cm} \]

2. **Rear Wheel Radius**:
\[ R_{\text{rear}} = \frac{154}{2} = 77 \, \text{cm} \]

### Step 3: Calculate the circumference of both wheels
The circumference \(C\) of a circle is given by the formula:
\[ C = 2 \pi r \]

1. **Circumference of Front Wheel**:
\[ C_{\text{front}} = 2 \times \frac{22}{7} \times 31.5 = 198 \, \text{cm} \]

2. **Circumference of Rear Wheel**:
\[ C_{\text{rear}} = 2 \times \frac{22}{7} \times 77 = 484 \, \text{cm} \]

### Step 4: Calculate the distance traveled by the rear wheel in 40 minutes
The rear wheel is rotating at \(24 \frac{6}{11}\) revolutions per minute. First, we convert this mixed number into an improper fraction:

1. **Convert to Improper Fraction**:
\[ 24 \frac{6}{11} = \frac{24 \times 11 + 6}{11} = \frac{264 + 6}{11} = \frac{270}{11} \, \text{revolutions per minute} \]

2. **Total Revolutions in 40 Minutes**:
\[ \text{Total revolutions} = \frac{270}{11} \times 40 = \frac{10800}{11} \approx 981.82 \, \text{revolutions} \]

3. **Distance Traveled by Rear Wheel**:
\[ \text{Distance} = \text{Total revolutions} \times C_{\text{rear}} = \frac{10800}{11} \times 484 \, \text{cm} \]

To convert this distance into meters:
\[ \text{Distance} = \frac{10800 \times 484}{11} \, \text{cm} = 4752 \, \text{m} \]

### Final Answer
The distance traveled by the tractor in 40 minutes is **4752 meters**.

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