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)
Responses
69.16 minutes
69.16 minutes
5.32 minutes
5.32 minutes
2.44 minutes
2.44 minutes
9.01 minutes
Let the rate at which Leonardo manufactures spark plugs be represented by x.
Sumaya's rate is 1/13 (since she can manufacture 1 spark plug in 13 minutes), and Leonardo's rate is 1/x.
When they work together, their rates add up to 1/5.32 (since they can manufacture 1 spark plug in 5.32 minutes).
So the equation is 1/13 + 1/x = 1/5.32.
To solve for x, we need to find a common denominator:
(1/13)x + 1 = (1/5.32)x
Now, multiply every term by 13*5.32 to eliminate denominators:
5.32x + 13 = 13*5.32
5.32x = 13*5.32 - 13
5.32x = 69.16 - 13
5.32x = 56.16
Now, divide both sides by 5.32 to isolate x:
x = 56.16 / 5.32
x ≈ 10.56
Rounded to the nearest hundredth, Leonardo's rate is approximately 10.56 minutes.
Therefore, the correct answer is 10.56 minutes.
To calculate the rate at which Leonardo manufactures spark plugs, we can set up a rational equation using the information given:
Let x be the rate at which Leonardo manufactures spark plugs (measured in minutes per spark plug).
The combined rate of Sumaya and Leonardo is given as 1/13 + 1/x, and this combined rate is equal to 1/5.32 since it takes them 5.32 minutes to manufacture a spark plug together.
So, we have the equation:
1/13 + 1/x = 1/5.32
To solve for x, we can cross multiply and simplify:
5.32 + 13 = 13x
18.32 = 13x
Dividing both sides by 13:
18.32/13 = x
Rounded to the nearest hundredth, x ≈ 1.41.
Therefore, Leonardo manufactures spark plugs at a rate of approximately 1.41 minutes per spark plug.
To find Leonardo's manufacturing rate, we can set up a rational equation using the given information.
Let x represent Leonardo's manufacturing rate in spark plugs per minute.
When Sumaya works alone, she can manufacture a spark plug in 13 minutes, so her manufacturing rate is 1 spark plug / 13 minutes, which can be written as 1/13.
When Leonardo helps her, they can manufacture a spark plug in 5.32 minutes, so their combined manufacturing rate is 1 spark plug / 5.32 minutes, which can be written as 1/5.32.
Since we want to find Leonardo's manufacturing rate, we can set up the equation:
1/13 + 1/x = 1/5.32
To solve this equation for x, we can multiply both sides by the least common denominator, which is 13*x*5.32:
(13*x*5.32 * 1/13) + (13*x*5.32 * 1/x) = (13*x*5.32 * 1/5.32)
Canceling out similar terms, we get:
5.32*x + 5.32 = 13
Simplifying further:
5.32*x = 13 - 5.32
5.32*x = 7.68
Dividing both sides by 5.32, we find:
x ≈ 7.68 / 5.32
x ≈ 1.44
Therefore, Leonardo's manufacturing rate is approximately 1.44 spark plugs per minute. Rounding this to the nearest hundredth, we get 1.44 minutes, which is closest to the option:
2.44 minutes