Verified Answer :

  • Identify the distance \(d = 30 \text{ cm}\) and time \(t = 2 \text{ minutes}\).
  • Define pace as the ratio of time to distance: \(\text{Pace} = \frac{t}{d}\).
  • Calculate the pace: \(\frac{2}{30} = \frac{1}{15} \text{ minutes per cm}\).
  • The final pace is \(\boxed{\frac{1}{15} \text{ min/cm}}\).

Explanation

  1. Problem Analysis and Definitions

To determine the ant's pace, we first identify the given information: the distance traveled is \(d = 30 \text{ cm}\) and the time taken is \(t = 2 \text{ minutes}\). The pace is defined as the time taken per unit of distance, which means we need to calculate the ratio of time to distance: \(\text{Pace} = \frac{\text{Time}}{\text{Distance}}\).

  1. Calculating the Pace

We use the values identified: \(t = 2 \text{ minutes}\) and \(d = 30 \text{ cm}\). Plugging these into the formula, we get:
\[\text{Pace} = \frac{2 \text{ minutes}}{30 \text{ cm}}.\]
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[\text{Pace} = \frac{2 \div 2}{30 \div 2} = \frac{1}{15} \text{ minutes per cm}.\]
This means the ant travels at a pace of \(\frac{1}{15}\) minutes per centimeter.

  1. Conclusion

The ant's pace is \(\frac{1}{15}\) minutes per centimeter, which is the time required for the ant to cover 1 centimeter of distance.
\(\boxed{\frac{1}{15} \text{ min/cm}}\)

Examples

Pace is a useful concept in various real-life scenarios, such as athletics or transportation planning. For instance, if a runner wants to know how long it takes them to run 1 kilometer, they calculate their pace in minutes per kilometer. In this ant example, knowing the pace of \(\frac{1}{15} \text{ min/cm}\) allows us to quickly predict how long it would take the ant to travel any other distance, such as 45 cm, simply by multiplying the distance by the pace: \(45 \text{ cm} \times \frac{1}{15} \text{ min/cm} = 3 \text{ minutes}\).

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