Concept 1 · free preview
Work = rate × time
Understand
Work questions are really rate questions. If someone finishes a whole job in n days, they do 1/n of it every day.
Rule
One day's work = 1 ÷ total days
Work done = one day's work × days
Work left = 1 − work done
Example
A finishes a job in 12 days. Work in 4 days = 4/12 = 1/3 Work left = 1 − 1/3 = 2/3 → A needs 8 more days.
Example
A does 2/5 of a job in 6 days. Whole job = 6 × 5/2 = 15 days.
Common mistake
Never add the days. If A takes 10 days and B takes 15, together they do not take 25 days — working together takes less time, not more.
Check yourself
A does 3/4 of a job in 9 days. How long for the whole job?
Answer: 12 days. (9 × 4/3)