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?(1 point)
5.32 minutes
9.01 minutes
2.44 minutes
69.16 minutes
Let's assume x is the rate at which Leonardo manufactures spark plugs.
According to the given information, Sumaya can manufacture a spark plug in 13 minutes, so her rate is 1/13 products per minute.
When Leonardo helps her, it takes them 5.32 minutes, so their combined rate is 1/5.32 products per minute.
Since Sumaya and Leonardo are working together, their combined rate should be the sum of their individual rates.
So, we can write the equation: 1/13 + x = 1/5.32.
To solve this equation, we can find the least common denominator by multiplying 13 and 5.32:
13 * 5.32 = 69.16
We can now rewrite the equation using the least common denominator:
(69.16/13) + x = 1/5.32
Simplifying this equation, we get:
5.32(69.16/13) + 5.32x = 1
69.16 * 5.32 + 5.32x = 1
x = (1 - 69.16 * 5.32)/5.32
Evaluating the right side of the equation, we get:
x ≈ -67.16
Since it doesn't make sense for the rate to be negative, the reasonable rate at which Leonardo manufactures spark plugs is approximately 0.00.
Rounded to the nearest hundredth, the correct answer is 0.00 which is equivalent to 2.44 (option 3).
it was 9.01 dumb bot
Apologies for the mistake. Let's reevaluate the equation to find the correct answer.
We have the equation (1/13) + x = 1/5.32.
To solve for x, let's subtract (1/13) from both sides:
x = 1/5.32 - 1/13.
To find a common denominator, we multiply 5.32 and 13:
x = 13/69.16 - 5.32/69.16.
Simplifying the equation:
x = (13 - 5.32)/69.16.
x = 7.68/69.16.
x ≈ 0.111, rounded to the nearest hundredth.
Therefore, the correct answer is 0.11, which is equivalent to 9.01 (option 2).
To find the rate at which Leonardo manufactures spark plugs, we can use the formula:
Rate = 1 / Time
Let's calculate the rate:
Rate = 1 / 5.32 minutes
Rate ≈ 0.188 (rounded to the nearest hundredth)
Therefore, the correct answer is 0.19 minutes, which is closest to 0.188 minutes.
To solve this problem using a rational equation, we can assume the rate of Sumaya alone as "x" spark plugs per minute, and the rate of Leonardo alone as "y" spark plugs per minute.
We know that Sumaya takes 13 minutes to manufacture a spark plug, so her rate would be 1 spark plug per 13 minutes, or x = 1/13.
When Leonardo helps Sumaya, together they can manufacture a spark plug in 5.32 minutes. So their combined rate would be 1 spark plug per 5.32 minutes, or (x + y) = 1/5.32.
Now we can solve for Leonardo's rate, y.
(x + y) = 1/5.32
(1/13 + y) = 1/5.32
To simplify, we need to find a common denominator.
13 * 5.32 = 69.16
Multiplying both sides of the equation by 69.16, we get:
69.16 * (1/13 + y) = 69.16 * (1/5.32)
Simplifying, we have:
5.32 + 69.16y = 13
Rearranging the equation to solve for y, we get:
69.16y = 13 - 5.32
69.16y = 7.68
y = 7.68 / 69.16
y ≈ 0.11
So, Leonardo manufactures spark plugs at a rate of approximately 0.11 spark plugs per minute.
Therefore, the correct answer, rounded to the nearest hundredth, is 0.11 minutes.