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### A Time-Rate Problem

```
Date: 8/14/96 at 10:32:18
From: Anonymous
Subject: A Time-Rate Problem

A can finish a project in 1.5 years, B in 1 year, and C in 9 months;
how long does it take to finish if A, B, and C work together?

Thanks,
Sg
```

```
Date: 8/30/96 at 17:14:19
From: Doctor Jerry
Subject:  A Time-Rate Problem

The key to problems like this is to notice how much of the project can
be done by each of A, B, and C in a common time period.

If A can finish in 1.5 (=3/2) years, then A can do 2/3 of the project
in 1 year.

If B can finish in 1 year, then B can do 1/1 of the project in 1 year.

If C can finish in 9 months (3/4 year), then C can do 4/3 of the
project in 1 year.

Working together, they can do 2/3 + 1/1 +4/3 = 3 projects in 1 year.
So, they can finish 1 project in 1/3 of a year.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Word Problems

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