3
Combined one day work = 1/12 + 1/18 = (3+2)/36 = 5/36
4
Time taken together = 36/5 = 7.2 days
Alternative (Shortcut): Time = (12 × 18)/(12 + 18) = 216/30 = 7.2 days
Worked Example 2: A and B together can complete work in 6 days. A alone can complete it in 10 days. In how many days can B alone complete the work?
1
Combined one day work = 1/6
3
B's one day work = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15
4
B alone can complete work in 15 days
Shortcut Formula: If A and B together complete work in T days and A alone in A days, then B alone takes: B = (A × T)/(A - T) days
Applying: B = (10 × 6)/(10 - 6) = 60/4 = 15 days
Most Common Trap: Students often add time instead of adding rates. Remember - when people work together, their RATES add up, not their TIME. If A takes 4 days and B takes 6 days, together they DON'T take 4+6=10 days. Instead, calculate 1/4 + 1/6 to find combined rate