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### Rates and Proportion

```
Date: 7/11/96 at 8:10:9
From: Anonymous
Subject: Rates and Proportion

10 men can build 2 boats in 4 days. Hom many men are needed to build 5
boats in 2 days?
```

```
Date: 7/11/96 at 9:16:57
From: Doctor Patrick
Subject: Re: Rates and Proportion

First we need to figure out how long it takes a man to build a boat,
and then we can apply that information to the question.

If 10 men can build 2 boats in 4 days then the same 10 men should be
able to build 1 boat in 2 days, since they would be building half as
many boats in half as much time.  Does this make sense?

Then we can also say that if 10 men can build 1 boat in 2 days then 20
men should be able to build a boat in 1 day, since twice the number of
men should be able to work twice as fast, right?

This would also mean that 1 man would take 20 days to build 1 boat.

Now we reverse the process and use this information to figure out how
many men are needed to build 5 boats in two days.

It would take one man 100 days to build five boats (20 days per boat*5
boats). If we want to cut this time down to 2 days we will need to
increase the number of men by the same amount that we cut the time.
Since the time is to be divided by 50 (100/50=2), we need to multiply
the number of men by 50 also.

Since 1 (the number of men who could build the boats in 100 days)
times 50 = 50, it will take 50 men to build 5 boats in two days.

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

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