How Do You Use Dimensional Analysis to Convert Units on Both Parts of a Rate?

We want to convert our rate from miles/hour to feet/second
mi is the abbreviation for miles
hr is the abbreviation for hours
ft is the abbreviation for feet
Multiplying by feet/miles will cancel miles in the numerator to give us feet/hour
Multiplying by hours/second will cancel the hour unit and give us feet/second!
Our conversion factors will need to have feet/miles and hours/second as their units
There are 5280 feet in 1 mile
There are 3600 seconds in 1 hour

1. 72 miles/1 hour is our original rate
2. A rate is just a ratio of two quantities measured in different units
3. A conversion factor is a number we use to change a quantity from one measurement to another
1. We need to figure out how we are going to get our units into feet/second
2. So our first conversion factor will have the units feet/mile
3. Our second conversion factor will have the units hours/second
1. We just figured out what units we need for our conversion factors
2. Now let's find the relationship between feet and miles, and between hours and seconds
3. Remember, a conversion factor is a number we use to change a quantity from one measurement to another
4. 5280 feet/mile is our first conversion factor
5. Since we need the units to be feet/miles, put 5280 ft on the top and 1 mi on the bottom
6. 1 hour/3600 seconds is our second conversion factor
7. Since we need the units to be hours/second, put 1 hr on the top and 3600 sec on the bottom
1. Our original rate was 72 miles/hour, and we need to get this into feet/second
2. Our conversion factors are 5280ft/1mi and 1hr/3600sec
3. 72•5280•1 = 380,160
4. 1•1•3600 = 3600
5. 380,160/3600 = 105.6
6. The miles unit in the numerator will cancel with the miles unit in the denominator
7. The hours units will also cancel out and we'll get feet/second
1. So our original rate of 72 miles/hour is the same as the rate 105.6 feet/second
2. The miles and hours units canceled out and we were left with feet/second!

A car is traveling 72 miles per hour on the interstate. How many feet per second is the car traveling?