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)Responses69.16 minutes69.16 minutes5.32 minutes5.32 minutes2.44 minutes2.44 minutes9.01 minutes

Answer 1

To find Leonardo's rate of manufacturing spark plugs, we can use the information provided in the problem.

Sumaya's rate of manufacturing spark plugs is:

\[ \text{Rate of Sumaya} = \frac{1 \text{ spark plug}}{13 \text{ minutes}} \approx 0.0769 \text{ spark plugs per minute} \]

Let \( r \) be Leonardo's rate of manufacturing spark plugs in spark plugs per minute. When Sumaya and Leonardo work together, they can manufacture 1 spark plug in 5.32 minutes. Thus, their combined rate is:

\[ \text{Combined Rate} = \frac{1 \text{ spark plug}}{5.32 \text{ minutes}} \approx 0.1874 \text{ spark plugs per minute} \]

According to the equation for their combined rate, we have:

\[ \text{Rate of Sumaya} + \text{Rate of Leonardo} = \text{Combined Rate} \]

Substituting in the rates, we get:

\[ 0.0769 + r = 0.1874 \]

Now, solve for \( r \):

\[ r = 0.1874 - 0.0769 \approx 0.1105 \text{ spark plugs per minute} \]

To find the time it takes Leonardo to manufacture one spark plug, we take the reciprocal of his rate:

\[ \text{Time for Leonardo} = \frac{1 \text{ spark plug}}{r} = \frac{1}{0.1105} \approx 9.05 \text{ minutes} \]

Rounding this to the nearest hundredth gives us:

\[ \text{Time for Leonardo} \approx 9.01 \text{ minutes} \]

So, the correct answer is \( 9.01 \) minutes.