Work problems involve calculating how long it takes for individuals or groups to complete a task, either separately or together. The standard model is:
If a person or machine can complete a task in $x$ hours, the rate of work is:
When multiple agents work together:
Another type of work problem involves man-hours or man-days as a unit of work. These problems assume the total work remains the same, and the number of workers and time vary.
The equation is based on the principle that:
This can be applied as:
This method is especially useful when the number of workers or amount of work changes across different scenarios.
An experienced roofer can roof a house in 26 hours. A beginner roofer needs 39 hours to complete the same job. Find how long it takes for the two to do the job together? Ans. 15.6 hours
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A contractor estimates that he could finish the project in 15 days if he has 20 men. At the start, he hired 10 men, then after 6 days, 10 more men are added. How many days was the project delayed? Ans. 3 days
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A swimming pool can be filled by an inlet pipe in 10 hours and emptied by an outlet pipe in 12 hours. One day, the pool is empty and the owner opens the inlet pipe to fill the pool, but he forgets to close the outlet. With both pipes open, how long would it take to fill the pool? Ans. 60 hours
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Mary, Sue, and Bill work at a motel. If each worked alone, it would take Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day, Mary came to work early and she had cleaned for 2 hours when Sue and Bill arrived and all three finished the job. How long did they take to finish? Ans. 2.6 hours
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