Mow the Lawn
A man begins to mow his lawn which is 100 feet by 100 feet. The lawn mower has a 36 inch cut and the man mows around the outer edge, working closer to the center on each successive lap.
After which lap, will the mowing be the closest to being half finished?
After which lap, will the mowing be the closest to being half finished?
posted by Zaux at
9:30 PM
10 Comments:
15 laps?
hi Knightmare ....
not 15 ...
(100-15*2)sq=1% more than half
oh...wait,3 feet with each pass=5 laps
This post has been removed by the author.
1 100 94 1164 1164
2 94 88 1092 2256
3 88 82 1020 3276
4 82 76 948 4224
5 76 70 876 5100
columns: lap, h, v, this lap, total mowed.
so after five laps :)
After Lap 5 he will have 4900 sq ft left... more than half finished.
Lap---size---ft^2left
0----100x100--10000
1----94 94-----8836
2----88 88-----7744
3----82 82-----6724
4----76 76-----5776
5----70 70-----4900
.
;
.
16----4 -4------16
As looking for an approximation. When done half, there will be a
square in the middle of half the area => 5000 sf ft => a side
length of 70.71 feet. So have reduced the width from 100 to 70.71
feet, that's 14.64 feet mown per side. That's equivalent to
14.64/3 ≈ 4.88 strips per side => 4.88 laps (approx). So it looks
pretty likely 5 laps would be the closer to half mown than 4 laps.
Double check: 4 laps would reduce width of unmown grass by 8*3
= 24 feet => unmown area = (100-24)² = 5776. 5 laps would reduce
the width of unkmown lawn by 10*3 = 30 feet => unmown area =
(100-30)² = 4900. This is much closer to half (5000), so 5 laps
it is.
5.3 laps. Did that in my head, so probably wrong.
5 laps it is ....
and Knightmare, you have the dinstinct honor of being the first to reveal the solution :)
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