01 Key Concepts
Work Rate
If a person can finish a job in n days, their work rate is 1/n of the job per day.
Combined Work Rate
When working together, add individual work rates: 1/a + 1/b = combined rate.
Time Together
Time to finish together = 1 / (combined rate).
Work Done in a Given Time
Work done = Rate x Time.
Efficiency Comparisons
A person who is 'twice as efficient' does the work in half the time (double the rate).
03 Key Formulas
- Rate = 1/Time to complete alone
- Combined rate = Rate1 + Rate2 + ...
- Time together = 1/Combined rate
04 Solved Examples
Example 1 A can finish a job in 6 days and B in 12 days. How long will they take together?
- A's rate = 1/6 per day, B's rate = 1/12 per day.
- Combined rate = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4.
- Time together = 1 / (1/4).
Answer: 4 days
Example 2 A does a job in 8 days alone. How much work does A do in 3 days?
- Rate = 1/8 per day.
- Work in 3 days = 3 x (1/8).
Answer: 3/8 of the job
Example 3 A is twice as efficient as B. Together they finish a job in 4 days. Find how long A alone would take.
- Let B's rate = x, so A's rate = 2x.
- Combined rate = 2x + x = 3x = 1/4.
- x = 1/12, so A's rate = 2/12 = 1/6.
- A alone takes 1/(1/6) = 6 days.
Answer: 6 days
05 Practice Questions
1A finishes a job in 10 days, B in 15 days. Find combined time.
6 days
2A's rate is 1/5 per day. How much does A do in 2 days?
2/5 of the job
3A finishes a job in 4 days, B in 4 days. Find combined time.
2 days
4A does a job alone in 12 days. In how many days would A finish half the job?
6 days
5A is 3 times as fast as B. If B takes 9 days alone, find A's time alone.
3 days
📄 Time & Work — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.