Rates add
If A completes a job in 12 days, A does 1/12 of it per day. Rates of workers working together add up. Equivalently, assume the total work is the LCM of the days, and count units per day.
Worked example
A takes 12 days and B takes 24 days. Take total work as 24 units. A does 2 units a day and B does 1 unit a day, so together 3 units a day. Time = 24 รท 3 = 8 days.
Variations
Pipes filling and emptying a tank use the same idea, with emptying as a negative rate. Efficiency problems say that one worker is, for example, twice as efficient as another, which gives you the ratio of rates directly.
Related topics
Strengthen the basics with ratio and proportion. See how this topic features in the banking quantitative section.
