Overview:
Work problems are types of problems that deal with people or machines that work at different rates of speed. Many of them use a formula that is similar to motion problems. The formula w=rt is used relating the rate of work, time, and the work done. Solving story problems involving work combines the steps of reading the story problem, extracting essential data, organizing data into an equation, and solving the equation.
Reading the Story Problem
Story problems ask questions involving days, hours, or minutes of work. The problem may have people working together or apart to complete a job, as well as the length of time it takes them. Some problems may have machines or objects that work at different rates to complete the same job. For example, suppose that a smaller pipe A can empty a pool in 5 hours. A larger pipe B can empty the pool in 3 hours. How long will it take both pipes together to empty the pool?
Extracting Essential Data
The solution to this problem is to write an equation that expresses the time it takes both the smaller pipe and the larger pipe to complete the job of emptying the pool. In this example, after 1 hour, Pipe A will empty 1/5 of the pool, and Pipe B will empty 1/3 of the pool. In other words, after 1 hour both pipes will empty 1/3 + 1/5 of the pool, or 5/15 + 3/15 or 8/15 of the pool.
Organizing Data into an Equation
Let t equal the amount of time it takes to empty the pool. It will take Pipe A t/5 to empty the pool and Pipe B t/3 to empty the pool. It will therefore take both pipes together t/3 +t/5 =1 to empty the pool. Since both fractions must have a common denominator, 5t/15 + 3t/15 = 1 or 8t/15 = 1, or 8t = 15.
Solving the Equation
If 8t =15, then it will take t = 15/8 hours to empty the pool using both pipes, or 1.875 hours to empty the pool. That is about 1 hour and 52 ½ minutes, because .875 of 60 minutes is 52 ½ minutes.
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