around a fence

• Sep 11th 2006, 02:36 PM
around a fence
Randy & his sister agreed that they would each mow one-half of the lawn. the lawn is a 25'x45' rectangle. the lawn mower cuts a path 2 ft. wide. if randy starts at one corner and mows a path completely around the outside, how many times should he go around to mow one half of the lawn?
• Sep 11th 2006, 02:54 PM
Quick
Quote:

Randy & his sister agreed that they would each mow one-half of the lawn. the lawn is a 25'x45' rectangle. the lawn mower cuts a path 2 ft. wide. if randy starts at one corner and mows a path completely around the outside, how many times should he go around to mow one half of the lawn?

After mowing once there will be a 21'x41' rectangle left to do, in other words, each time he goes around once the dimensions will shrink by 4 feet.

The area of a 25x45 foot rectangle is 1125, half of that would be 562.5

Now write out a table...

Dimensions of Rectangle...................Area

25x45...........................................11 25
21x41...........................................86 1
17x37...........................................62 9

So he will go around a bit more than 2 times.
• Sep 11th 2006, 02:57 PM
dan
Quote:

Originally Posted by Quick
After mowing once there will be a 23'x43' rectangle left to do, in other words, each time he goes around once the dimensions will shrink by 2 feet.

The area of a 25x45 foot rectangle is 1125, half of that would be 562.5

Now write out a table...

Dimensions of Rectangle...................Area

25x45...........................................11 25
23x43...........................................98 9
21x41...........................................86 1
19x39...........................................74 1
17x37...........................................62 9
15x35...........................................52 5

So he will go around a bit less than 5 times.

dan
• Sep 11th 2006, 03:01 PM
Quick
Quote:

Originally Posted by dan
dan

You just have to make things complicated :rolleyes:

Although I don't know a formula, I get the answer to be 2.3078703703703703703703703... times around the yard
• Sep 11th 2006, 03:54 PM
• Sep 11th 2006, 04:06 PM
Quick
Quote:

2.3078703703703703703703703...

But are you concerned with the method of getting there?
• Sep 11th 2006, 04:07 PM
topsquark
Quote:

Originally Posted by Quick
After mowing once there will be a 23'x43' rectangle left to do, in other words, each time he goes around once the dimensions will shrink by 2 feet.

Note that if you go around the perimeter mowing a 2 ft. wide path the new dimensions will be less by 4 ft., not 2 ft., because we are taking off 2 ft. from each side of the rectangle. You need to take this change into account.

-Dan

SOMEwhere on the forum is a nearly exact copy of the same problem. I can't seem to find it. (I've never gotten the hang of using the search feature on this thing.) Perhaps someone else will have better luck looking for it.
• Sep 11th 2006, 04:11 PM
Quick
Quote:

Originally Posted by topsquark
Note that if you go around the perimeter mowing a 2 ft. wide path the new dimensions will be less by 4 ft., not 2 ft., because we are taking off 2 ft. from each side of the rectangle. You need to take this change into account.

-Dan

Darn, I missed that. I've changed my posts with the correction.

PS I've never been able to get the search thing to work :mad: