Answer:
(72/17) hours
Step-by-step explanation:
Time Jackie would take alone , J = 8 hrs
Time Patricia would take alone , P = 9 hrs
Let the time they will take together be T
use the formula for shared unit rate
[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{J}[/tex] + [tex]\frac{1}{P}[/tex]
[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{T}[/tex] = [tex]\frac{17}{72}[/tex]
T = [tex]\frac{72}{17}[/tex] hours (or 4.24 hours)
It takes them to work together for 4 hours and 14 minutes.
A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given
Jackie was to paint her living room alone. It would take 8 hours.
Her sister Patricia could do the job in 9 hours.
How long would it take them to work together?
We know the work is inversely proportional to the time. And formula we have
[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{T_1} +\dfrac{1}{T_2}[/tex]
We have
[tex]\rm T_1 = 8, \ \ \ and\ \ T_2 = 9[/tex]
Then by the formula.
[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{8} +\dfrac{1}{9}\\\\\rm \dfrac{1}{T_f} = \dfrac{8+9}{8*9} \\\\\rm \dfrac{1}{T_f} = \dfrac{17}{72} \\\\T_f \ = \dfrac{72}{17}\\\\T_f \ = 4.24[/tex]
Then the time 4.24 will be 4 hours and 14 minutes.
Thus, it takes them to work together for 4 hours and 14 minutes.
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