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If A can finish a work in 20 days and B in 30 days, how many days will they take if they work together?
12 days
15 days
10 days
25 days
12 days
Use the product-over-sum formula for two workers: 20+3020├Ч30тАЛ=50600тАЛ=12 days.
A can finish the work in 20 days and B can finish the work in 30 days.
Time=A+BA├ЧBтАЛ
Use the product-over-sum formula for two workers: 20+3020├Ч30тАЛ=50600тАЛ=12 days.
Students often make the mistake of averaging the days or adding them directly (20+30=50), forgetting that individual work rates must be added, not the days.
Calculate Individual Work Rates
A's 1 day work is 201тАЛ and B's 1 day work is 301тАЛ of the total work.
WorkAтАЛ=201тАЛ,WorkBтАЛ=301тАЛ
Add Combined Work Rates
Add the individual rates to find their combined 1 day work: 201тАЛ+301тАЛ=605тАЛ=121тАЛ.
201тАЛ+301тАЛ=121тАЛ
Determine Total Days
Invert the combined 1 day work to find the total number of days required to finish the work together: 12 days.
Total┬аDays=121тАЛ1тАЛ=12┬аdays
A is correct because working together they take 12 days.
This concept of combining rates is identical to solving pipe and cistern problems and relative speed calculations.
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