Question

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?

Answer 1

Answer:  7.8 days

Step-by-step explanation:

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