CalcElfCalcElf › Two road crews: 20 and 30 days alone
Two road crews: 20 and 30 days alone
One crew alone can pave a road in 20 days, and a second crew alone can pave the same road in 30 days. Working together, how many days do they need?
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
Each crew's daily rate is 1 divided by its own time, and working together the rates add, so the shared time is 1 divided by the sum of the two rates.
Common mistakes
- Averaging 20 and 30 days.
- Subtracting the two rates instead of adding them.