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forsale [732]
3 years ago
13

A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days

later the coworker joins in to help finish the job, how many days does it take to paint the building?
Mathematics
1 answer:
Sonja [21]3 years ago
7 0

Answer:  7.8 days

<u>Step-by-step explanation:</u>

Painter can get the job done in 15 days so gets \dfrac{1}{15} of the job done in 1 day.

Coworker can get the job done in 10 days so gets \dfrac{1}{10} of the job done in 1 day.

Together, they get \dfrac{1}{15}+\dfrac{1}{10} of the job done in 1 day.

Painter worked for 3 days so completed \dfrac{1}{15}(3)=\dfrac{1}{5} of the job.

That leaves a remaining of 1-\dfrac{1}{5}=\dfrac{4}{5} of the job to be completed.

Let x represent the number of days it will take them to work together.

Painter + Coworker = Together

\dfrac{1}{15}(x)\quad +\quad \dfrac{1}{10}(x)\quad =\quad \dfrac{4}{5}

Multiply by 30 to eliminate the denominator:

\dfrac{1}{15}(x)(30) +\ \dfrac{1}{10}(x)(30) = \dfrac{4}{5}(30)

Simplify and solve for x:

    2x + 3x = 24

            5x = 24

              x=\dfrac{24}{5}

              x = 4.8

Remember that Painter worked 3 days alone in addition to the 4.8 days they worked together.

So the total time to paint the building is 3 + 4.8 = 7.8

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