Following the boundary of a rectangular field, it requires 11 rounds of a lawn mower to cut 1/2 of it and 14 more to cut the remainder. If the lawn mower cuts a swath 2 feet wide and all the swaths are full, what are the dimentions of the field? Thanks and good luck.
The man starts at one corner and cuts a strip A down the entire length of the field. Next, he cuts strip B, then strip C and D, and is now ready to start on strip E. Although the strips, A,B,C, and D are all of different lengths, he has cut an area which is equal to the difference in area of 2 rectangles.
Since it requires: 11+14 =25 rounds to cut the field and each round consists of 2 swaths, each 2 feet wide, then the width of the field is: 25 x (2x2) =100 feet. The 11 rounds represent 22 swaths of 2 feet each, or: 22 x 2 =44 feet. Hence, the width of the area remaining is: 100 - 44 =56 feet. Now, if L represents the length of the field, then:(L - 44) x 56 equals the area remaining. But the remaining area is 1/2 the total area, which equals: 1/2(100L) =50L. Therefore, (L - 44) x 56 = 50L, or 6L =2,464 and L =2,464/6 =410 2/3 feet, which is the length of the field. And so, the field is: 100 by 410 2/3 feet.
And that is the end of this challenge!!!.
