Applications of Rational Expressions

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In this section, we review how to solve word problems when rational expressions are involved. The most common problems in this section are motion word problems and rate of work problems. Motion word problems remain simple: we are relating distance to the product of speed and time. We will see many problems that involve a current or wind speed in this section. These problems are generally solved by realizing the wind or current in a person’s favor, will increase their speed. Alternatively, the wind or current against a person’s favor will decrease their speed. Additionally, we will tackle a problem known as rate of work. Rate of work problems are fairly simple to solve. They involve analyzing two or more people’s individual contributions to obtain a combined speed for a given job. We usually begin these problems by finding each person’s rate of work per one unit of time. We can then combine these individual rates in the scenario to find the group’s rate of work in one unit of time. After this is done, we can use a variable to represent the number of given units of time to complete the job. We multiply the group’s rate of work in one unit of time by this variable and set this equal to one. The one here refers to one completed job. Solving for the variable gives us the number of given units to complete the job if everyone is contributing at their given rate of work.
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