Calculate Running Pace: Converting 2km in 4½ Minutes to Minutes per Kilometer

To solve this problem, we need to calculate the average time Chris spends running per kilometer. We are given that Chris runs 2 km in $4\frac{1}{2}$ minutes.

First, let's convert the mixed fraction $4\frac{1}{2}$ into an improper fraction. The whole number 4 and the fraction $\frac{1}{2}$ combine as follows:

$4\frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}$

This means that the total time taken is $\frac{9}{2}$ minutes.

Next, we find the average time Chris runs per kilometer by dividing the total time by the distance:

$\text{Average time per km} = \frac{\text{Total time}}{\text{Total distance in km}} = \frac{\frac{9}{2}}{2}$

To divide by a fraction, we multiply by its reciprocal:

$\frac{\frac{9}{2}}{2} = \frac{9}{2} \times \frac{1}{2} = \frac{9}{4}$

The fraction $\frac{9}{4}$ can be converted back into a mixed number:

$\frac{9}{4} = 2\frac{1}{4}$

Therefore, the average time Chris runs per kilometer is $2\frac{1}{4}$ minutes.