Unit rate is defined as rate with a denominator of $1$ unit. If a sprinter runs $100$ meters in $10.49$ seconds, her speed per second can be calculated as shown below. (Note that this was the world record set in 1988 by Florence Griffith-Joyner at the US Olympic Trials.)

$\frac { 100 \text{ m }} { 10.49 \text{ sec} } = \frac { x \text{ m }} { 1 \text{ sec} }$ gives $x = 9.53$, so she ran $9.53$ meters each second. This is a unit rate. 

In addition, the number of seconds it takes her to run each meter can be calculated as $\frac { 10.49 \text{ sec} } { 100 \text{ m} } = \frac { x \text{ sec} } { 1 \text{ m} }$ gives $x = 0.1049$, so it took her $0.1049$ seconds to run each meter.

1. An ice skater covered $1500$ meters in $106.43$ seconds. Find his unit rate of speed in meters per second.

   Step 1(a):

   $\frac{1500}{106.43}=\frac{x}{1}$

   Step 2(a):

   $106.43x = 1500$

   Answer (a):

   $x = \text{ about } 14$ meters per second

2. A train in Japan can travel $813.5$ miles in $5$ hours. Find the unit rate of speed in miles per hour.

   Hint (b):

   Follow the steps in part (a) and in the example above.

3. Alaska has a very low population density. It only has $655{,}000$ people in $570{,}374$ square miles. Find the unit rate of density in terms of people per square mile.

   Answer (c):

   About $1.15$ people per square mile.

4. New Jersey has a very high population density. It has $1{,}171$ people per square mile. If Alaska had the same population density as New Jersey, what would be the population of Alaska? Solve with a proportion. (By the way, there were about $307{,}000{,}000$ people in the United States as of the year 2009.)

   Hint (d):

   $\frac{1,171\text{ people}}{1\text{ sq mile}}=\frac{x \text{ people}}{570,374\text { sq miles}}$