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Machine A can produce a batch of components in 15 days, while Machine B can produce the same batch in 20 days. If they work together, how many days will it take to complete the batch?
8.5 days
8.6 days
8.7 days
8.8 days
8.6 days
Use the product over sum formula directly for two workers: T=15+2015├Ч20тАЛ=35300тАЛ=760тАЛ days, which simplifies to approximately 8.57 or 8.6 days.
Machine A time = 15 days, Machine B time = 20 days
T=x+yx├ЧyтАЛ
Use the product over sum formula directly for two workers: T=15+2015├Ч20тАЛ=35300тАЛ=760тАЛ days, which simplifies to approximately 8.57 or 8.6 days.
Students often wrongly calculate the average time as (15+20)/2=17.5 days instead of using the reciprocal work rate method.
Find Individual Work Rates
Machine A can complete 1/15 of the batch per day, and Machine B can complete 1/20 of the batch per day.
RateAтАЛ=151тАЛ,RateBтАЛ=201тАЛ
Calculate Combined Work Rate
Add the individual rates of Machine A and Machine B to find their combined one-day work output.
Combined┬аRate=151тАЛ+201тАЛ=604+3тАЛ=607тАЛ
Calculate Total Time
Take the reciprocal of the combined work rate to find the total number of days required to complete the batch together.
T=760тАЛтЙИ8.57┬аdays
B is correct because working together they take 60/7 days which rounds to 8.6 days.
This inverse proportion concept is identical to problems involving pipes and cisterns or relative speeds in time-speed-distance.
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