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A and B can finish a project in 20 days. B alone can finish it in 30 days. How many days will A take to finish the project alone?
60
40
50
45
60
Use the product-over-difference formula: 30тИТ2020├Ч30тАЛ=10600тАЛ=60 days.
Combined time of A and B = 20 days, Time taken by B alone = 30 days
TAтАЛ=TBтАЛтИТTA+BтАЛTA+BтАЛ├ЧTBтАЛтАЛ
Use the product-over-difference formula: 30тИТ2020├Ч30тАЛ=10600тАЛ=60 days.
Students often add the days (20+30=50) or subtract incorrectly without inverting rates first.
Determine 1-day work rates
The combined 1-day work of A and B is 201тАЛ and B's 1-day work is 301тАЛ.
WorkA+BтАЛ=201тАЛ,WorkBтАЛ=301тАЛ
Calculate A's 1-day work
Subtract B's rate from the combined rate to find A's individual 1-day work: 201тАЛтИТ301тАЛ=601тАЛ.
WorkAтАЛ=201тАЛтИТ301тАЛ=601тАЛ
Calculate total days for A
Invert A's 1-day work rate to find the total time required for A to finish the project alone.
TAтАЛ=60┬аdays
A is correct because A takes 60 days to complete the project alone.
Pipe and cistern problems use the exact same fractional rate logic, where inlet and outlet speeds substitute for workers.
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