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If A can complete a piece of work in 15 days and B can complete the same work in 20 days, how long will they take to complete the work working together?
8.57┬аdays
7.5┬аdays
9┬аdays
10┬аdays
8.57┬аdays
Use the product/sum formula: (15├Ч20)/(15+20)=300/35=60/7. Calculating 60/7 gives approximately 8.57 days.
Time taken by A to complete the work = 15 days. Time taken by B to complete the work = 20 days.
T=A+BA├ЧBтАЛ
Use the product/sum formula: (15├Ч20)/(15+20)=300/35=60/7. Calculating 60/7 gives approximately 8.57 days.
Many students mistakenly calculate the average of the days (15+20)/2=17.5 or simply add the days, ignoring the inverse relationship between speed and time.
Define variables
Let A's time be t1тАЛ=15 and B's time be t2тАЛ=20.
t1тАЛ=15,t2тАЛ=20
Apply combined work formula
When two people work together, the combined time is the product of their individual times divided by the sum of their individual times.
T=15+2015├Ч20тАЛ
Simplify and Calculate
Simplifying the expression: T=300/35, which reduces to 60/7.
T=760тАЛтЙИ8.57┬аdays
A is correct because the combined time calculated using the formula T=(A├ЧB)/(A+B) yields 60/7, which is approximately 8.57 days.
This concept of combined rate is identical to problems involving two pipes filling a tank or two resistors connected in parallel in a physics circuit (1/ReqтАЛ=1/R1тАЛ+1/R2тАЛ).
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