Rate


 * TASK: Look back at your flashcard for rate. Explain "rate" in your own words.**

Rate is a comparison of two different units. It's written as a fraction and can be divided.

The most common form of rate you will see is speed. This type of rate tells you how fast something happens (for example, how fast a car is going, how quickly a person can type, how fast someone runs, the speed at which a biker is riding, etc). However, you may see some exceptions such as how far a car goes on a gallon of gas or how far someone

**How do we find rate?**

Rate is written as a fraction (which means that we have to divide). The numerator is one of the units that we're comparing and the denominator is the other. We can tell what goes in the numerator and what goes in the denominator by what the question is asking for. The denominator is whatever unit you're trying to find 1 of. The numerator is the unit you're comparing it to.

When we're talking about speed, the numerator is the number of whatever units we're measuring in (for example, miles, feet, words, inches) and the denominator is the amount of time.

//Be careful// because sometimes the units given in the problem are not the same units they're looking for in the answer and we might have to do an extra step to change the units!


 * Example 1:** It takes Tammy 45 minutes to ride her bike 5 miles. How long will it take her to ride her bike 8 miles?

In the problem, the units we're comparing are minutes and miles. In order to answer the question, we need to know how long it will take Tammy to ride her bike for 1 mile. Therefore, the miles is going to be in the denominator. So, we get:

Rate = = 9 minutes per 1 mile

This means that is takes Tammy 9 minutes to ride her bike 1 mile. We can use this information to determine how long it will take Tammy to ride her bike 8 miles by multiplying 9 and 8. This gives us 72, so our answer is that it takes Tammy 72 minutes to ride her bike for 8 miles.


 * Example 2:** In a game of ice hockey, the hockey puck took 0.8 seconds to travel 89 feet to the goal line. Determine the average speed of the puck in feet per second.

The units we're comparing here are seconds and feet. According to the question we want to know how many feet the puck travels in 1 second (feet per second), so the feet will be in the numerator and the seconds will go in the denominator. So, we get:



Therefore, we can say that the puck travels 111.25 feet per second.


 * What's this going to look like on the Regents?**

On the Regents, we most often see rate problems written as word problems. When we're solving these problems, we need to pick out the key information (determining importance) that's going to help us find the rate.

We need to know: 1. What are the units we're comparing? 2. Which unit are we trying to find 1 of? (This unit will become the denominator and the other unit will become the numerator).

**TASK: Explain in your own words how we find rate.**


 * Key Words for Rate:** If you see any of these words, the problem is most likely asking you find the rate:

How fast... How quickly... Rate... Speed... units per other unit (ex: miles per hour, words per minute, feet per second, miles per gallon, etc)

**TASK: Open the document and complete the practice Regents problems.**