CalcElfCalcElf › 20 days and 30 days: working together
20 days and 30 days: working together
A project can be completed by person A alone in 20 days, and by person B alone in 30 days. How many days will it take for both to complete it together?
Answer
12 days
Step-by-step
- 1 ÷ 20 = 0.05Work done per day by A
- 1 ÷ 30 = 0.0333Work done per day by B
- 1 ÷ (0.05 + 0.0333) = 12Combined time = 1 ÷ combined rate
Why it works
In work problems, the total amount of work is treated as 1. Each person's efficiency is the reciprocal of their days. When working together, efficiencies are added. Since days are the reciprocal of efficiency, you must first calculate the combined efficiency and then take its reciprocal; you cannot simply add or average the two numbers of days. The unit for this type of problem is "fraction of work completed per day". Writing it out clearly prevents mistakes.
Common mistakes
- Directly adding or averaging the two numbers of days, ignoring that efficiencies should be added.
- Treating efficiency as days and forgetting to take the reciprocal at the end.
- Making a mistake when finding a common denominator for fraction addition, causing the combined efficiency to deviate from the correct value.