working together, katherine and marina can sand a large cabinet in 2 hours. it would take katherine 10 hours…

working together, katherine and marina can sand a large cabinet in 2 hours. it would take katherine 10 hours to do the job alone. what is the value of r, the part of the job that marina can complete in 1 hour?\nrate (part/hour) time (hours) part of cabinet sanded\nkatherine $\frac{1}{10}$ 2 $\frac{2}{10}$\nmarina r 2 2r\n0.1\n0.4\n0.5\n0.6

working together, katherine and marina can sand a large cabinet in 2 hours. it would take katherine 10 hours to do the job alone. what is the value of r, the part of the job that marina can complete in 1 hour?\nrate (part/hour) time (hours) part of cabinet sanded\nkatherine $\frac{1}{10}$ 2 $\frac{2}{10}$\nmarina r 2 2r\n0.1\n0.4\n0.5\n0.6

Answer

Answer:

0.4

Explanation:

Step1: Set up the equation

Since they complete 1 job together in 2 hours, $\frac{2}{10}+2r = 1$.

Step2: Simplify the equation

First, simplify $\frac{2}{10}$ to $\frac{1}{5}$. So, $\frac{1}{5}+2r = 1$.

Step3: Isolate the variable term

Subtract $\frac{1}{5}$ from both sides: $2r=1 - \frac{1}{5}$.

Step4: Calculate the right - hand side

$1-\frac{1}{5}=\frac{5 - 1}{5}=\frac{4}{5}$. So, $2r=\frac{4}{5}$.

Step5: Solve for r

Divide both sides by 2: $r=\frac{4}{5}\div2=\frac{4}{5}\times\frac{1}{2}=\frac{4}{10} = 0.4$.