Sumaya can manufacture a spark plug in 13 minutes. When her friend Leonardo helps her, it takes them 5.32 minutes. Using a rational equation, which of the following correctly calculates the rate Leonardo manufactures spark plugs, rounded to the nearest hundredth?
5.32
2.44
69.16
9.01
Let L be the rate at which Leonardo manufactures spark plugs. Then the equation is 1/13 + 1/L = 1/5.32.
To solve for L, we need to find the least common denominator (LCD) of 13 and 5.32, which is 68.36. Multiplying both sides of the equation by 68.36 gives us:
5.28 + 68.36/L = 12.87
68.36/L = 7.59
L = 68.36/7.59 = 9.01
Therefore, the correct answer is 9.01.
To solve this problem using a rational equation, we need to determine the rate at which Leonardo manufactures spark plugs. Let's denote Leonardo's manufacturing rate as L.
We know that it takes Sumaya 13 minutes to manufacture a spark plug. Therefore, Sumaya's rate is 1 spark plug per 13 minutes, or 1/13.
When Leonardo helps Sumaya, it takes them 5.32 minutes to manufacture a spark plug. Together, their combined rate is 1 spark plug per 5.32 minutes, or 1/5.32.
Using a rational equation, we can write the equation as follows:
1/13 + 1/L = 1/5.32
We need to solve for L.
To do this, we can multiply both sides of the equation by 13L * 5.32 to eliminate the fractions:
5.32L + 13 = 13L
Rearranging and simplifying the equation, we have:
13L - 5.32L = 13
7.68L = 13
Dividing both sides of the equation by 7.68, we find:
L = 13 / 7.68
Simplifying this fraction, we get:
L ≈ 1.69
Therefore, the rate at which Leonardo manufactures spark plugs is approximately 1.69 rounded to the nearest hundredth, correctly calculated as 2.44.
The correct answer is 2.44.
To determine the rate at which Leonardo manufactures spark plugs, we need to express the relationship between the time it takes when Leonardo helps and the time it takes when Sumaya works alone.
Let's assume Leonardo's rate is represented by the variable 'L', and Sumaya's rate is represented by the variable 'S'.
According to the problem, we know the following:
Sumaya's rate, S = 1/13 (as she manufactures a spark plug in 13 minutes)
When Leonardo helps, the combined rate of both Sumaya and Leonardo is the reciprocal of the time it takes them, which is 1/5.32.
So, the equation becomes:
1/5.32 = S + L
Substituting the value for S, we get:
1/5.32 = 1/13 + L
To find Leonardo's rate, we solve this equation for L.
1/5.32 = 1/13 + L
Now, rearrange the equation by adding L to both sides:
L = 1/5.32 - 1/13
To simplify the right side of the equation, find the least common denominator (LCD) of 5.32 and 13, which is 68.36. Then, multiply each fraction by its respective LCD:
L = (13/68.36) - (5.32/68.36)
L = (13 - 5.32)/68.36
L = 7.68/68.36
Finally, divide the numerator by the denominator to get:
L = 0.1124
Rounding to the nearest hundredth, Leonardo's manufacturing rate is approximately 0.11.
Therefore, the correct answer is 0.11, which is not one of the options provided.