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?

 7.8 days

Step-by-step explanation:

Painter can get the job done in 15 days so gets of the job done in 1 day.

Coworker can get the job done in 10 days so gets of the job done in 1 day.

Together, they get of the job done in 1 day.

Painter worked for 3 days so completed of the job.

That leaves a remaining of of the job to be completed.

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

Painter + Coworker = Together

Multiply by 30 to eliminate the denominator:

Simplify and solve for x:

    2x + 3x = 24

            5x = 24

              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

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

step-by-step explanation:

b and c