1. 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?

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.

3. 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

4. Originally Posted by dan
dan
You just have to make things complicated

Although I don't know a formula, I get the answer to be 2.3078703703703703703703703... times around the yard

5. Thx! But Whats The Answer?

6. Originally Posted by The Answer
2.3078703703703703703703703...
But are you concerned with the method of getting there?

7. 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.

8. 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