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Algebra II Chapter 9 Applications: Work
If a painter can paint a room in 4 hours, how much of the room can the painter paint in 1 hour? 1 / 4 of the room 1 / 4 is the painter’s rate of work. This is the part of the task that is completed in 1 unit of time. A pipe can fill a tank in 30 minutes. What is the pipe’s rate of work? 1 / 30 A second pipe can fill a tank in x minutes. What is the second pipe’s rate of work? 1/x
In solving a work problem, the goal is to determine the time it takes to complete a task. The basic equation that is used to solve work problems is… Rate of Work * Time Worked = Part of Task Completed For example, if a faucet can fill a sink in 6 minutes, in 5 minutes, what part of the task will be completed? Rate of Work = 1 / 6 Time Worked = 5 minutes Part of Task Completed = 5 / 6
1. Both Ulf and Jerzy can mow their grandparents’ lawn in 30 minutes working alone. If they worked together, how long would it take to mow the lawn? Ulf’s Rate of Work: 1 / 30 Jerzy’s Rate of Work: 1 / 30 Answer: Working together, they could mow the lawn in only 15 minutes.
2. A painter can paint a ceiling in 60 minutes. The painter’s apprentice can paint the same ceiling in 90 minutes. How long will it take to paint the ceiling if they work together? Painter’s Rate of Work: 1 / 60 Apprentice’s Rate of Work: 1 / 90 Answer: They can paint the ceiling in 36 minutes if they work together.
3. A small water pipe takes four times longer to fill a tank than does a large water pipe. With both pipes open, it takes 3 hours to fill the tank. Find the time it would take the small pipe, working alone, to fill the tank. Large Pipe’s Rate of Work: 1 / x Small Pipe’s Rate of Work: 1 / 4 x Answer: The small pipe could fill the tank in 15 hours if it was working alone.
4. Two computer printers that work at the same rate are working together to print the payroll checks for a corporation. After they work together for 3 hours, one printer quits. The second printer requires 2 more hours to complete the checks. Find the time it would take one printer, working alone, to print all the checks. Printer #1’s Rate of Work: 1 / x Printer #2’s Rate of Work: 1 / x Answer: Each printer could print all the checks in 8 hours working by themselves.