Simultaneous EquationsDate: 08/10/97 at 12:31:29 From: Anonymous Subject: Simultaneous equations A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days. If A and C work together, the job will take 8 days. In how many days can each man working alone do the job? Date: 08/10/97 at 16:00:41 From: Doctor Anthony Subject: Re: Simultaneous equations Let A do 1/a part of the job in 1 day. A could do the whole job in a days. Let B do 1/b part of the job in 1 day. B could do the whole job in b days. Let C do 1/c part of the job in 1 day. C could do the whole job in c days. In 1 day, working together, they do 1/a + 1/b + 1/c = 1/6 ..... (1) of the job. Similarly 1/b + 1/c = 1/9 ..... (2) and 1/a + 1/c = 1/8 ..... (3) From these three equations we solve for 1/a, 1/b and 1/c. Subtracting (3) from (1) 1/b = 1/6 - 1/8 = 1/24 Subtracting (2) from (1) 1/a = 1/6 - 1/9 = 1/18 then from (2) 1/c = 1/9 - 1/24 = 5/72 From these a = 18 days b = 24 days c = 72/5 = 14.4 days -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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