$2017$
days
$10$
days
$209$
days
$34$
days

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1st2ndGOATSFIELD OF GRASS EATENTIME (DAYS)The table above show us some indirectly and directly proportional quantities, that can be interpreted as: How much more days, more field of grass eaten, that can be eaten by less goats. So we have the equation:

${10 \over x} = {10 \over 2017} \times {2017 \over 10}$

${10 \over x} = {1}$

$x = 10$

The answer is $10$ days.