Final answer:
The actual length of the Darling Downs Rabbit Board fence is calculated by converting the map scale and the fence measurement to improper fractions and then multiplying them. The result is that the fence is 620 miles long in reality.
Step-by-step explanation:
To find the actual length of the Darling Downs Rabbit Board fence, we use the scale given on the map and multiply it by the fence's measurement on the map. The scale is 1 inch = 70 6/7 miles, and the map shows the fence as 8¾ inches long.
First, convert the mixed numbers to improper fractions:
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- The scale becomes 1 inch = 70 6/7 miles = 496/7 miles.
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- The fence measurement becomes 8¾ inches = 35/4 inches.
Next, multiply the scale by the fence measurement to find the actual length:
(496/7 miles/inch) × (35/4 inches) = (496 × 35) / (7 × 4) miles
Simplify the multiplication:
(496 × 35) / (7 × 4) = 17,360 / 28 miles
Simplify the fraction:
17,360 / 28 = 620 miles
Therefore, the actual length of the Darling Downs Rabbit Board fence is 620 miles.