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Rufus appears before Bill and Ted and offers them a bogus proposition: they must paint a house together with their magical guitars in a mere 5 hours. Ted, who is tired, knows that the fastest he can solo rock the paint job through the strings of his guitar is 19 hours. How hard does Bill have to jam to ensure the house is completed in time? Give your answer as the number of hours Bill must play; write your answer as a decimal rounded to two places, without any units.

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opudodennis

Answer:

6.79

Step-by-step explanation:

-Let X denote the total amount of the job.

-The job has to be done in 5 hrs, therefore the portion done every hour is:

[tex]Rate=\frac{Total}{Time}\\\\=\frac{X}{5}\\\\=\frac{1}{5}X=0.2X[/tex]

Therefore, the rate of Bill and Ted working jointly must equal the rate calculated above:

[tex]R_{Bill}=\frac{X}{19}\\\\=\frac{1}{19}X\\\\R_{Bill}+R_{Ted}=R_{required}\\\\\frac{1}{19}X+R_{Ted}=\frac{1}{5}X\\\\R_{Ted}=\frac{1}{5}X-\frac{1}{19}X\\\\=\frac{14}{95}X\\\\\therefore \frac{14}{95}X=1\ hr\\\\X=1\div \frac{14}{95}\\\\=6.7857\approx 6.79[/tex][tex]hrs[/tex]

Hence, Bill working alone should complete the house in 6.79 hrs

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