Question

question #17 working together, amanda and micaela can organize a garage in 5.74 hours. if amanda had organized the garage on her own, it would have taken her 12 hours. write an equation to model this situation and then determine how long it will take micaela to organize the garage by herself. round your answer to the nearest hundredth. o $\frac{1}{12}+\frac{1}{x}=\frac{1}{5.74}$ it will take 11 hours for micaela to organize the garage by herself. o $\frac{1}{12}+\frac{1}{5.74}=\frac{1}{x}$ it will take 3.88 hours for micaela to organize the garage by herself. o 5.74 + 12 = x it will take 17.74 hours for micaela to organize the garage by herself. o 5.74 + x = 12 it will take 6.26 hours for micaela to organize the garage by herself.

Explanation:

Step1: Define work - rate

Let the time it takes Micaela to organize the garage alone be $x$ hours. The work - rate of Amanda is $\frac{1}{12}$ (jobs per hour) since she can complete 1 job in 12 hours. The work - rate of Micaela is $\frac{1}{x}$ (jobs per hour), and their combined work - rate is $\frac{1}{5.74}$ (jobs per hour) as they can complete 1 job in 5.74 hours together.

Step2: Set up the equation

The sum of their individual work - rates equals their combined work - rate. So, the equation is $\frac{1}{12}+\frac{1}{x}=\frac{1}{5.74}$.

Step3: Solve the equation for $x$

First, subtract $\frac{1}{12}$ from both sides:
$\frac{1}{x}=\frac{1}{5.74}-\frac{1}{12}$
Find a common denominator, which is $5.74\times12 = 68.88$.
$\frac{1}{x}=\frac{12 - 5.74}{68.88}=\frac{6.26}{68.88}$
Then, take the reciprocal of both sides:
$x=\frac{68.88}{6.26}\approx11$

Answer:

The correct option is: $\frac{1}{12}+\frac{1}{x}=\frac{1}{5.74}$, It will take 11 hours for Micaela to organize the garage by herself.