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)
1. 9.01 minutes
2. 69.16 minutes
3. 5.32 minutes
4. 2.44 minutes
Let L be the rate at which Leonardo manufactures spark plugs.
The equation based on the given information is 1/13 + 1/L = 1/5.32.
Multiplying both sides of the equation by 13L*5.32, we get 5.32L + 5.32(13) = 13L.
Simplifying the equation, we have 5.32L + 68.96 = 13L.
Subtracting 5.32L from both sides of the equation, we get 68.96 = 7.68L.
Dividing both sides of the equation by 7.68, we get L = 8.95 minutes.
Rounding L to the nearest hundredth, we get L ≈ 9.01 minutes.
Therefore, option 1, 9.01 minutes, correctly calculates the rate Leonardo manufactures spark plugs.
To solve this problem, we can set up a rational equation using the idea that rates are equal to the reciprocal of the time it takes.
Let's use the variable "x" to represent Leonardo's rate of manufacturing spark plugs.
Sumaya's rate of manufacturing is 1 plug per 13 minutes: 1/13.
When they work together, their combined rate is 1 plug per 5.32 minutes: 1/5.32.
Sumaya's rate + Leonardo's rate = Combined rate
1/13 + x = 1/5.32
To solve for x, multiply both sides of the equation by 13*5.32 to eliminate the denominators:
5.32 + 13x = 13/5.32
Now, we can solve for x:
13x = 1/5.32 - 5.32
13x = 1/5.32 - 5.32/5.32
13x = 1 - 5.32/5.32
13x = (5.32 - 5.32)/5.32
13x = 0/5.32
x = 0
Therefore, Leonardo's rate is 0 spark plugs per minute.
None of the options provided are correct.
To find the rate at which Leonardo manufactures spark plugs, we can set up a rational equation as follows:
Rate of Leonardo + Rate of Sumaya = Total Rate
Let's say the rate at which Leonardo manufactures spark plugs is represented by x (in minutes per spark plug). We know that the rate of Sumaya is 1 plug per 13 minutes. So we have:
x + 1/13 = 1/5.32
To solve this equation for x, we need to isolate it on one side. First, we can subtract 1/13 from both sides:
x = 1/5.32 - 1/13
Next, let's find a common denominator for the two fractions on the right-hand side, which is 5.32 * 13 = 69.16:
x = 13/69.16 - 5.32/69.16
Simplifying the fractions:
x = (13 - 5.32) / 69.16
x = 7.68 / 69.16
Now, we can divide to find the decimal value of x:
x ≈ 0.111
So, rounding to the nearest hundredth, the rate at which Leonardo manufactures spark plugs is approximately 0.11 minutes per spark plug.
Therefore, the correct answer is option 4: 2.44 minutes.