Time and Work Problems

If a task takes 10 hours to complete, how much of the task can be finished in 2 hours?

Worker A can finish a job in 6 hours, whereas Worker B can finish it in 4 hours. How long will it take both workers to complete the job together?

If three workers can complete a job in 8 hours, how long will it take six workers to complete the same job?

A single worker can complete a task alone in 12 days. If two workers cooperate on the task, how long will it take them to finish it?

If 4 workers can complete a job in 10 hours, how many workers are needed to complete the same job in 5 hours?

Work Completion and Rates

A task requiring 10 hours means that in 2 hours, 20% of the task can be completed.
Worker A’s rate is 1 job in 6 hours, translating to 1/6 of a job per hour.
Worker B’s rate is 1 job in 4 hours, equating to 1/4 of a job per hour.
Working together, their combined rate is 1/6 + 1/4 = 5/12 of a job per hour.
Thus, both workers together can complete the job in 12/5 hours or 2.4 hours.

Workforce Dynamics

Three workers can finish a job in 8 hours, which indicates their combined rate is 1 job in 8 hours (1/8 jobs/hour).
When doubled to six workers, their rate becomes 6 × (1/8) = 6/8 = 3/4 jobs/hour.
Consequently, six workers can complete the same job in 4 hours (1 job / (3/4 jobs/hour)).

Cooperation in Task Completion

A single worker can finish a task alone in 12 days, meaning their daily rate is 1/12 of the job.
When two workers cooperate, their combined rate is 1/12 + 1/12 = 1/6 of the job per day.
Therefore, working together, they will complete the job in 6 days (1 job / (1/6 jobs/day)).

Worker Efficiency

With 4 workers completing a job in 10 hours, each worker's contribution is 1/10 of the job in an hour collectively (1/4 jobs/hour per worker).
To finish the same job in 5 hours, the required rate is 1 job / 5 hours = 1/5 jobs/hour.
Doubling the efficiency to reach this output will necessitate 8 workers (1/5 jobs/hour / (1/4 jobs/hour per worker)).

This quiz covers various problems related to time and work efficiency. You'll tackle questions about how different numbers of workers can affect the time taken to complete tasks. Test your understanding of work rates and collaborative efficiency with practical scenarios.