How Do You Use Dimensional Analysis to Convert Units on One Part of a Rate?

Rate is a ratio of two quantities measured in different units
The units we're starting with are miles per hour, and we need feet per hour, so we need to change miles to feet
There are 5280 feet in 1 mile
5280 feet/1 mile and 1 mile/5280 feet are two conversion factors we could multiply our rate by to convert our units
When you multiply miles/hour by feet/mile, the miles cancel out and you're left with feet/hour as the units
Using 5280 feet/1 mile will cancel out the miles in our original rate
72•5280 = 380,160

1. Rate is a ratio of two quantities measured in different units
2. In our problem, the rate is 72 miles per 1 hour
3. We have miles per hour, and we need feet per hour, so we need to change miles to feet
1. A conversion factor is a number that is used to convert a quantity in a given measurement to a different measurement
2. There are 5280 feet in one mile
3. We could write the conversion factor two different ways: 5280 feet/1 mile or 1 mile/5280 feet
4. But we need to pick the one that will help us convert our rate to feet per hour
5. Since our rate has miles in the numerator, we want a conversion factor with miles in the denominator
6. Then the miles will cancel out, so we want to use 5280 feet/1 mile
1. Rate is a ratio of two quantities measured in different units
2. Our rate in this problem was 72 miles per 1 hour
3. A conversion factor is a number that is used to convert a quantity in a given measurement to a different measurement
4. The conversion factor we are using is 5280 feet per 1 mile
5. So we need to multiply 72 miles/hour by 5280 feet/mile
6. It's important to keep the units as part of the problem!
7. When you multiply mi/1hr by ft/mi, the miles cancel out and you're left with ft/hr as the units
1. In order to figure out how many feet the car is traveling per hour, multiply 72 by 5280
1. 72•5280 = 380,160

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