Time and Work Problems

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)).