Calculate the Average Speed: A Snail's Journey in Time and Distance

To solve this problem, we will calculate the average speed of the snail by considering both its movement and rest periods. The average speed is calculated using the formula:

$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$.

Let's break down the calculation:

• Step 1: Calculate the distance covered during the first crawling period.
  The snail crawls at 4 cm/min for 7 minutes. Thus, the distance covered in this period is:

  $4 \, \text{cm/min} \times 7 \, \text{min} = 28 \, \text{cm}$.

• Step 2: Note the rest period.
  The snail rests for 3 minutes. This time needs to be included in the total time calculation.

• Step 3: Calculate the distance and time covered in the second crawling period.
  The snail crawls 30 cm in 12 minutes. Hence:

  Distance in this period is $30 \, \text{cm}$, and the time is $12 \, \text{min}$.

• Step 4: Calculate the total distance.
  Total distance = $28 \, \text{cm} + 30 \, \text{cm} = 58 \, \text{cm}$.

• Step 5: Calculate the total time.
  Total time = $7 \, \text{min (crawling)} + 3 \, \text{min (rest)} + 12 \, \text{min (crawling)} = 22 \, \text{min}$.

• Step 6: Calculate the average speed using the total distance and time.

  $\text{Average speed} = \frac{58 \, \text{cm}}{22 \, \text{min}} \approx 2.64 \, \text{cm/min}$.

Therefore, the average speed of the snail is $2.64$ cm per minute.