Ratio of Rates and Work
Date: 06/06/98 at 20:38:49 From: Eugene Ni Subject: Maths Problem: Ratio and Proportion Dear Dr. Math, Here's the question: Four skilled workers can do a job in 5 days. Five semi-skilled workers can do the same job in 6 days. How long does it take 1 skilled and 2 semi-skilled workers to do the job together? I've tried this question several times, using inverse proportion, but it doesn't work out. Thanks, Eugene
Date: 06/06/98 at 20:54:04 From: Doctor Gary Subject: Re: Maths Problem: Ratio and Proportion Let's look at each type of worker separately, with the goal of determining what fraction of a job one such worker will do in one day: 4 skilled workers can do a job in 5 days Since it takes them 5 days, they do 1/5 of the job in each day. Since there are 4 of them, each does 1/20 of the job in one day. 5 semi-skilled workers can do the same job in 6 days Since it takes them 6 days, they do 1/6 of the job in each day. Since there are 5 of them, each does 1/30 of the job in each day. So the rate of work for a skilled worker is 1/20 of the job per day, and the rate of work for a semi-skilled worker is 1/30 of the job per day. Since we have 1 skilled worker and 2 semi-skilled workers, the combined rate of work is: 1/20 + 1/30 + 1/30 = (3+2+2)/60 = 7/60 of the job per day Since rate of work is defined as the quotient of work divided by time: r = w/t time must be the quotient of work divided by rate: t = w/r When we divide 1 job by 7/60 of the job per day, the answer is 60/7 of a day, or 8 and 4/7 days. Checking our answer: - In 60/7 days, the skilled worker will do (60/7)(1/20), or 3/7, of the job. - In 60/7 days, each semi-skilled worker will do (60/7)(1/30), or 2/7, of the job. So two semi-skilled workers will do 4/7 of the job. Together, the whole team will do 7/7 of the job in 60/7 days. -Doctor Gary, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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