BitWithBite
Arithmetic (Beginner) · Quick Reference
Time & Work Cheat Sheet
In one line: time and work problems figure out how long a task takes when different people or machines work at different rates, alone or together.
Key Ideas
1Work Rate. If a person can finish a job in n days, their work rate is 1/n of the job per day.
2Combined Work Rate. When working together, add individual work rates: 1/a + 1/b = combined rate.
3Time Together. Time to finish together = 1 / (combined rate).
4Work Done in a Given Time. Work done = Rate x Time.
5Efficiency Comparisons. A person who is 'twice as efficient' does the work in half the time (double the rate).
Worked Examples
A can finish a job in 6 days and B in 12 days. How long will they take together?
4 days
A does a job in 8 days alone. How much work does A do in 3 days?
3/8 of the job
A is twice as efficient as B. Together they finish a job in 4 days. Find how long A alone would take.
6 days
Formulas
Rate = 1/Time to complete alone
Combined rate = Rate1 + Rate2 + ...
Time together = 1/Combined rate
Practice Yourself
A finishes a job in 10 days, B in 15 days. Find combined time.
6 days
A's rate is 1/5 per day. How much does A do in 2 days?
2/5 of the job
A finishes a job in 4 days, B in 4 days. Find combined time.
2 days