Work-rate problem: One worker can complete a job in 4 hours. A second worker is twice as fast. How long to complete the job together?

Work-rate problem: One worker can complete a job in 4 hours. A second worker is twice as fast. How long to complete the job together?

• A. 30 minutes
• B. 1 hour
• C. 1 hour 15 minutes
• D. 1 1/3 hours

Answer: (D)

When two workers combine on a task, you add their rates. The first worker finishes the job in 4 hours, so their rate is 1/4 of the job per hour. The second worker is twice as fast, so their rate is 2 × 1/4 = 1/2 of the job per hour. Together, they complete 1/4 + 1/2 = 3/4 of the job each hour. To find the total time, take the reciprocal of the combined rate: 1 ÷ (3/4) = 4/3 hours. That’s 1 hour and 1/3 of an hour, which is 1 hour and 20 minutes. So the job is finished in 1 1/3 hours.

When two workers combine on a task, you add their rates. The first worker finishes the job in 4 hours, so their rate is 1/4 of the job per hour. The second worker is twice as fast, so their rate is 2 × 1/4 = 1/2 of the job per hour. Together, they complete 1/4 + 1/2 = 3/4 of the job each hour.

To find the total time, take the reciprocal of the combined rate: 1 ÷ (3/4) = 4/3 hours. That’s 1 hour and 1/3 of an hour, which is 1 hour and 20 minutes. So the job is finished in 1 1/3 hours.