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Questions and Answers
In time and work problems, what does the term 'work' refer to?
In time and work problems, what does the term 'work' refer to?
- The effort put in by the workers
- The time taken to finish a task
- The resources required for the task
- The task to be completed (correct)
If a person can complete a task in 6 hours, while another person can complete the same task in 8 hours, how long will it take them to complete the task together?
If a person can complete a task in 6 hours, while another person can complete the same task in 8 hours, how long will it take them to complete the task together?
- 3 hours
- 5 hours
- 7 hours
- 4 hours (correct)
If a machine can complete a task in 10 hours, how long will it take for 5 machines to complete the same task?
If a machine can complete a task in 10 hours, how long will it take for 5 machines to complete the same task?
- 50 hours
- 2 hours (correct)
- 10 hours
- 4 hours
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Study Notes
Time and Work Problems
- In time and work problems, the term 'work' refers to the task or job that needs to be completed.
Work Rate and Task Completion
- If a person can complete a task in 6 hours, their work rate is 1/6 of the task per hour.
- If another person can complete the same task in 8 hours, their work rate is 1/8 of the task per hour.
- When they work together, their combined work rate is the sum of their individual work rates: (1/6 + 1/8) = 7/24 of the task per hour.
- To find the time it takes for them to complete the task together, invert the combined work rate: 24/7 = 3.43 hours.
Machine Efficiency
- If a machine can complete a task in 10 hours, its work rate is 1/10 of the task per hour.
- If 5 machines work together, their combined work rate is 5 times the individual work rate: 5 x 1/10 = 1/2 of the task per hour.
- To find the time it takes for 5 machines to complete the task, invert the combined work rate: 2/1 = 2 hours.
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