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### Mowing Half a Lawn

```
Date: 03/31/2002 at 11:45:04
From: Jessica Pion
Subject: Word Problem

Chris and Lee are each responsible for mowing half of their 50-foot
by 90-foot rectangular back yard. Chris starts mowing at an outside
corner, gradually working toward the middle by mowing around the
outside edges. If the mower cuts a 3-foot wide path, during which trip
around the yard should Chris stop and Lee start mowing?

I understand that the sides of the lawn get shorter every time Chris
goes around. I don't understand what formula I would use to figure
how much the lawn decreases.

Thank you,
Jessica Pion
```

```
Date: 03/31/2002 at 18:37:08
From: Doctor Ian
Subject: Re: Word Problem

Hi Jessica,

Let's draw a picture to help us visualize what's going on:

90
+----------------------------------+
|                                  |
|  +----------------------------+  |
|  |                            |  |
|  |  +----------------------+  |  |
|  |  |                      |  |  |
|  |  |                      |  |  | 50
|  |  |                      |  |  |
|  |  +----------------------+  |  |
|  |                            |  |
|  +----------------------------+  |
|                                  |
+----------------------------------+

Each of the strips is 3 feet wide, so after n trips around the yard,
thesituation looks like this:

90
+----------------------------------+
|                                  |
|  +----------------------------+  |
|  |                            |  |
|  |  +----------------------+  |  |
|  |  |      90 - 6n         |  |  |
|  |  |              50 - 6n |  |  | 50
|  |  |                      |  |  |
|  |  +----------------------+  |  |
|  |                            |  |
|  +----------------------------+  |
|                                  |
+----------------------------------+

So after some number of trips, the amount of yard left for Lois to
cut,

(90 - 6n)(50 - 6n)

is going to be less than half of the total amount of yard,

(1/2)(90)(50)

which means that you want to find n such that

(90 - 6n)(50 - 6n) <  (1/2)(90)(50)

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra
Middle School Word Problems

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