Podcast
Questions and Answers
In a work problem, the number 1 represents the total amount of work.
In a work problem, the number 1 represents the total amount of work.
True (A)
If t is the time working together, which expression represents the portion of the job that Ted will complete when he works with Galen?
If t is the time working together, which expression represents the portion of the job that Ted will complete when he works with Galen?
t/5
How long would it take Mr. Branches' son to rake the leaves on his own?
How long would it take Mr. Branches' son to rake the leaves on his own?
7.5 hours
How long will the three pipes, operating together, take to fill the tank?
How long will the three pipes, operating together, take to fill the tank?
What equation can be used to solve for t, the time to fill the empty cistern using all pipes?
What equation can be used to solve for t, the time to fill the empty cistern using all pipes?
How long will the Doe family take to fill their pool if they use their own hose along with their neighbor's?
How long will the Doe family take to fill their pool if they use their own hose along with their neighbor's?
How long will Jim and John take to paint the room if they work together?
How long will Jim and John take to paint the room if they work together?
How much of the manuscript can John write in 1 hour?
How much of the manuscript can John write in 1 hour?
How many hours would Laura take to type the manuscript working alone?
How many hours would Laura take to type the manuscript working alone?
How many hours will two experienced plumbers and three inexperienced plumbers take to do the job?
How many hours will two experienced plumbers and three inexperienced plumbers take to do the job?
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Study Notes
Work Problems Key Concepts
- In work problems, "1" symbolizes the total work to be accomplished.
Collaboration and Work Rates
- Ted's mowing time: 5 minutes; Galen's time: 15 minutes; together, they complete a job in variable time t; Ted's portion of work when combined is represented by t/5.
- Mr. Branches rakes leaves solo in 5 hours; with his son, they complete it in 3 hours; the son's solo time is 7.5 hours.
- Filling a tank: Pipe 1 fills in 24 minutes, Pipe 2 in 8 minutes, Pipe 3 in 12 minutes; all together, they fill it in 4 minutes.
Cistern and Filling Rates
- A cistern drain takes 6 hours; filled by two pipes that take 4 hours and 5 hours; the filling equation is 15x + 12x - 10x = 60.
Swimming Pool Filling Scenario
- The Doe family's pool filling time: their hose alone takes 12 hours; neighbor’s hose takes 30 hours; combined time is approximately 8.57 hours (8 4/7).
Painting and Typing Tasks
- Jim Roller paints a room in 3 hours; John Brush in 4 hours; together, they finish in 1.71 hours (1 5/7).
- John types 2/3 of a manuscript in 12 hours; his hourly rate is 1/18 of the manuscript.
- John writes 2/3 of a manuscript in 12 hours; with Laura's help, they finish in 2 hours, indicating that Laura alone takes 2.25 hours for the complete manuscript.
Plumbing Team Composition
- An experienced plumber completes a task in 8 hours; an inexperienced plumber takes 12 hours; two experienced and three inexperienced plumbers together finish the job in 2 hours.
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