# Constant Rate Word Problems

This book describes constant rate word problems. Everything You Need to Know About Constant Rate Word Problems begins from perhaps the easiest concepts to work with: a speedometer, odometer, and clock. Students have a high comfort level with relating travel time to driving speed to distance covered. In Everything You Need to Know About Constant Rate Word Problems we offer a path from this understandable starting point to an equivalent comfort level with various types of these word problems. Here are multiple examples with detailed, step-by-step instructions. Formulas and techniques are patiently derived for the reader rather than merely stated in order to bring lucidity and understanding.

This book is ideal for undergraduate algebra students in their first year of college. This is an amplified look at a class of word problems usually given three or so pages of coverage in a 100-level algebra textbook. Everything You Need to Know About Constant Rate Word Problems is an ideal adjunct to any standard text including word problems of this type.

## An Introduction to Constant Rate Word Problems

Constant rate word problems apply to life. They are models of easily understood, realistic scenarios like driving a car, flying a plane, painting a house, and so forth. We may need to determine speed over one leg of a multi-step trip, or with two or three workers, we need to determine how long it takes to finish a single project through shared effort. On the surface, these scenarios may not seem related. Presented here are the basic math concepts, understandable with even high-school level algebra, of how to handle these types of problems from the same fundamental principles. In typical presentations, constant rate word problems describing motion (walking, bicycling, flying, driving, etc.) and work completion (plowing a field, painting a house, digging a hole, etc.) are considered separately as different classes of problems. This treatment unites the different categories (“uniform motion”, “work problems”, etc.) with a holistic treatment around shared fundamentals.

The class of word problems covered here is common in intermediate algebra and often gives students problems, especially on timed tests. These problems involved time (duration), rate (such as speed), and some idea of “distance”. Distance may be a distance travelled or an amount of work processed. Distance travelled is perhaps the easiest concept to work with, so we will start with examples of this special case. These simpler cases are known as Uniform Motion problems. A reader having encountered them before may not have seriously considered the units of distance, rate, and time. In this text, a serious and formal consideration of units in examples with underscore how knowing the natural relationship of the units and keeping track of them carefully—something typically not done in standard texts—not only aids in comprehension but provides natural guidance to forming the necessary equations out of the problem text.

When a student first encounters the work-related problems in this category, they are often given an equation summing up fractions to be extracted from the word problem. The careful reader will have the benefit of knowing how that rational equation was derived and can be derived when needed by a deeper understanding of rate and the units of rate and conceptualizing work problems and motion problems.