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### 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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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