Simultaneous Equations

Date: 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
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