Question 277979: Four horses are tethered at the four corners of a square of side 14cm such that two horses along the same side can
just reach each other. They were able to graze the area in 11 days. How many days will they take in order to graze
the left out area?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area is a square with each side = 14 cm.
the area of the square is 14 * 14 = 196 cm^2.
each horse can consume grass in an area the size of 1/4 of the circle that each can make with their tether.
since their tether is equal to 1/2 of 14 = 7 cm, then the area each horse can graze is equal to 1/4 * pi * 7^2 = 38.48451001 cm^2.
since there are 4 horses, the total area they can graze while tethered is 4 * 38.48451001 cm^2 = 153.93804.
the area within the square that is left to graze is equal to 196 - 153.93804 cm^2 which equals:
42.06195997 cm^2.
since they were able to graze 153.93804 cm^2 in 11 days, then their rate of grazing is equal to:
153.93804 / 11 = 13.99436728 cm^2 per day.
42.06195997 / 13.99436728 = 3.005634992 days
At the rate of grazing that they showed over the 11 days, it would take them an additional 3.005634992 days to finish off the interior of the square assuming they were no longer tethered.
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