Work Problems

Work Problems

Work Problems

 

Work problems are another staple of algebra courses. A work problem is normally stated as two workers (two people, machines, hoses, drains, etc.) working together and working separately to complete a task. Often one worker performs faster than the other. Sometimes the problem states how fast each can complete the task alone and you are asked to find how long it takes for them to complete the task together. At other times, you are told how long one worker takes to complete the task alone and how long it takes for both to work together to complete it; you are asked how long the second worker would take to complete the task alone. The formula is quantity (work done—usually ‘‘1’’) ¼ rate times time: Q = rt. The method outlined below will help you solve most, if not all, work problems. The following chart is useful in solving these problems.

Increasing/Decreasing by a Percent - 12

Increasing/Decreasing by a Percent - 12

Mixture problems involve mixing two different concentrations to obtain some concentration in between. Often these problems are stated as alcohol or acid solutions, but there are many more types. For example, you might want to know how many pure peanuts should be mixed with a 40% peanut mixture to obtain a 50% peanut mixture. You might have a two-cycle engine requiring a particular oil and gas mixture. Or, you might have a recipe calling for 1% fat milk and all you have on hand is 2% fat milk and 1 2% fat milk. These problems can be solved using the method illustrated below.

Increasing/Decreasing by a Percent - 11

Increasing/Decreasing by a Percent - 11

Some money problems involve one quantity divided into two investments paying different interest rates. Such questions are phrased ‘‘How much was invested at ___%?’’ or ‘‘How much was invested at each rate?’’

Increasing/Decreasing by a Percent - 10

Increasing/Decreasing by a Percent - 10

Coin problems are also common algebra applications. Usually the total number of coins is given as well as the total dollar value. The question is normally ‘‘How many of each coin is there?’’

   Let x represent the number of one specific coin and put the number of other coins in terms of x. The steps involved are:

Increasing/Decreasing by a Percent - 9

Increasing/Decreasing by a Percent - 9

Grade computation problems are probably the most useful to students. In these problems, the formula for the course grade and all but one grade are 224 given. The student is asked to compute the unknown grade in order to ensure a particular course average.