You are at the center of square forest of 60 km width. If you decide to get out walking in straight lines with the route actually travelled as follows: 5 km south, then 10 km west, then 15 km north, 20 km east, 25 km south, and so on. How far would you have to walk before you get out of the forest? And which side of the forest would you exit?
Answers
South, 75 ,km
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Given : You are at the center of square forest of 60 km width.
you decide to get out walking in straight lines with the route actually travelled as follows: 5 km south, then 10 km west, then 15 km north, 20 km east, 25 km south, and so on.
To Find : How far would you have to walk before you get out of the forest? And which side of the forest would you exit
Solution:
You are at the center of square forest of 60 km width.
So u need to go 30 km either of north/south/east/west
travelled as follows: 5 km south, then 10 km west, then 15 km north, 20 km east, 25 km south,
Travelled to South = 5 - 15 + 25 - 35 + 45 - 55 = - 30 km South = 30 km North
Travelled to West = 10 - 20 + 30 - 40 + 50 = 30 km West
50 comes before 55 Hence he came out at 30 km West
so need not to travel 55 km.
till then Travelled to South = 5 - 15 + 25 - 35 + 45 = 25 km south
Hence He exit after 25 km South and 30 km West
So He exit west side
Total Distance covered = 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50
= 5 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= 5 * 10 * 11/2
= 275 km
Travelled 275 km
Exit on west side
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