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)

Question

5.32 minutes

9.01 minutes

2.44 minutes

69.16 minutes

Answer 1

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).

Answer 2

it was 9.01 dumb bot

Answer 3

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).