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Answer:
It will take 1.5 hours to paint the room together
Step-by-step explanation:
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours.
Work done by Martha in 1 hour = [tex]\frac{1}{2}[/tex]
Work done by Jamie in 1 hour = [tex]\frac{1}{6}[/tex]
Work one together in 1 hour = [tex]\frac{1}{2}+\frac{1}{6}[/tex]
Now take common denominator to add both fractions
LCD = 6, Multiply the first fraction by 3
[tex]\frac{1*3}{2*3}+\frac{1}{6}[/tex]
[tex]\frac{3}{6}+\frac{1}{6}[/tex]
Now add the numerators
[tex]\frac{4}{6}[/tex]
[tex]\frac{2}{3}[/tex]
To find total hours of painting together, we take reciprocal of 2/3
Time taken to paint together = [tex]\frac{3}{2}= 1.5[/tex]
It will take 1.5 hours to paint the room together
The nearest tenth of an hour, will it take them to paint the room together is 1.5 hours.
Given data:
Time taken by Martha to paint a room is, 2 hours.
Time taken by Jamie to pain the same room is, 6 hours.
Then work done by each of Martha and Jamie in 1 hour is given as,
[tex]W_{Martha}=\dfrac{1}{2}\\\\W_{Jamie}=\dfrac{1}{6}[/tex]
Total work done in 1 hour is given as,
[tex]W_{total}=W_{Martha} + W_{Jamie}\\\\W_{total}=\dfrac{1}{2} + \dfrac{1}{6}\\\\W_{total}=\dfrac{6+2}{12} \\\\W_{total}=\dfrac{8}{12}\\\\W_{total}=\dfrac{2}{3}[/tex]
To find total hours of painting together, we take reciprocal of 2/3.
Then, time taken to paint together is, 3/2 = 1.5 hours.
Thus, we can conclude in the nearest tenth of an hour, will it take them to paint the room together is 1.5 hours.
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https://brainly.com/question/15194302
