Farmer Bob is considering buying a new field that is next to one he already owns. The field he is considering is a perfect square. The fence along each side of this square field is made of old logs and is one-fourth of a mile long. If he can walk at a rate of four miles per hour, how long will it take him to inspect the fence all the way around this field?
The fence is one-fourth of a mile long on each side, so the fence around the field is 1/4 + 1/4 + 1/4 + 1/4 = 1 mile long.
It will take Farmer Bob 1 mile / 4 miles/hour = <<1/4/4=0.0625>>0.0625 hours to inspect the fence. Answer: \boxed{0.0625}.
To find the time it will take for Farmer Bob to inspect the fence around the field, we need to calculate the perimeter of the square field and then divide it by his walking speed.
A square has all four sides equal in length, so if each side of the field is one-fourth of a mile long, then the perimeter of the field will be the sum of the lengths of all four sides.
Since there are four sides of equal length, the perimeter is:
Perimeter = 4 * (length of one side)
Given that each side of the field is one-fourth of a mile long, the perimeter will be:
Perimeter = 4 * (1/4) = 1 mile
Now, to find the time it will take Farmer Bob to inspect the fence, we divide the perimeter by his walking speed:
Time = Perimeter / Walking speed
Given that his walking speed is four miles per hour, we have:
Time = 1 mile / 4 miles per hour
Simplifying, we find:
Time = 1/4 hour
Therefore, it will take Farmer Bob 1/4 hour, which is equivalent to 15 minutes, to inspect the fence all the way around the field.