1) 60 meters of fencing are needed to fence in a square lot. What is the area of the lot?
a) 3600 m^2
b) 900 m^2
c) 225 m^2
d) 15 m^2
2) A can do a piece of work in r days and B, who works faster, can do the same work in s days. Which of the following expressions, if any, represents the number of days it would take the two of them to do the work if they worked together?
a) r+s/2
b) r-s
c) 1/r + 1/s
d) rs/r+s
e) none of these answer
perimeter = 4 x
so x = 15
area = 225
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A does task/r per day
B does task/s per day
[ 1/r + 1/s ] task/day together
so
1/ [ 1/r + 1/s ]
= r s / (r+s)
or
r s
-------
r + s
which is probably d) but you left the parentheses out
yes
1) To find the area of the square lot, we need to know the length of each side of the square. Since a square has four equal sides, we can divide the total amount of fencing (60 meters) by 4 to find the length of one side.
Each side of the square would be 60/4 = 15 meters.
Now, to find the area of the square, we multiply the length of one side by itself.
Area = length x length = 15 x 15 = 225 square meters
Therefore, the area of the lot is 225 m^2.
The correct answer is option c) 225 m^2.
2) To find the number of days it would take for A and B to complete the work together, we need to determine their combined work rate.
A can complete the work in r days, which means A's work rate is 1 job per r days. B can complete the work in s days, so B's work rate is 1 job per s days.
To calculate their combined work rate, we add their individual work rates:
Combined work rate = 1/r + 1/s
The reciprocal of the combined work rate represents the number of days required for both A and B to complete the work together.
Number of days = 1 / (1/r + 1/s)
Simplifying the expression:
Number of days = 1 / ((s+r) / (rs))
Number of days = rs / (s+r)
Therefore, the correct answer is option d) rs / (s+r).
To solve question 1, we need to find the side length of the square lot using the given information about the fencing.
Let's assume the side length of the square lot is "x" meters. Since all four sides of a square are equal, the perimeter of the square would be 4 times the length of one side, which is 4x. According to the question, the perimeter is 60 meters, so we can write the equation:
4x = 60
To find the side length, we can divide both sides of the equation by 4:
x = 60/4
Simplifying this gives us:
x = 15
Now we know that the side length of the square lot is 15 meters. To find the area of the lot, we can square the side length:
Area = side length^2 = 15^2 = 225
Therefore, the area of the lot is 225 square meters. The correct answer is option c) 225 m^2.
To solve question 2, we need to determine the combined work rate of A and B working together.
A completes the work in r days, so the work rate of A would be 1 work per r days (1/r). Similarly, B completes the same work in s days, so the work rate of B would be 1 work per s days (1/s).
When A and B work together, their work rates are added. Therefore, the combined work rate of A and B is (1/r) + (1/s).
To find the number of days required for the two of them to complete the work when working together, we can take the reciprocal of this combined work rate:
Number of days working together = 1 / (1/r + 1/s)
To simplify this expression, we need to find the common denominator:
Number of days working together = 1 / ((s + r) / (rs))
Dividing by a fraction is equivalent to multiplying by its reciprocal, so we can rewrite the expression as:
Number of days working together = (rs) / (s + r)
Therefore, the correct answer is option d) rs / (r + s).