Together Jamie and Michael can paint the pool building in 9 hrs. From past Experience Jamie can paint the building in 2 hrs less than Michael. How long would each take to paint alone.

If Michael takes x, hours, then

1/x + 1/(x-2) = 1/9

Now just find x, and then x-2.

Thank you

Subtract the fraction and write our answer in lowest terms

4/5 -3/8
1/40
1 17/40
7/10
19/45

I think it is 1/40

To solve this problem, we can set up equations based on the given information.

Let's assume that Michael takes x hours to paint the building alone. Since Jamie takes 2 hours less, Jamie would take x - 2 hours.

We can now use the concept of work rates to create an equation. The work rate is the amount of work done per unit of time.

The work rate of a person is given by the inverse of the time it takes them to complete a task. So, Michael's work rate would be 1/x (1 unit of work divided by x hours), and Jamie's work rate would be 1/(x - 2).

According to the problem, when they work together, they can finish the task in 9 hours. This means that the combined work rate is 1/9.

Now, we can set up an equation using the work rates of Jamie and Michael:
1/x + 1/(x-2) = 1/9

To solve this equation, we can multiply through by 9x(x-2) to eliminate the denominators:
9(x-2) + 9x = x(x-2)

Simplifying further:
9x - 18 + 9x = x^2 - 2x

Combining like terms:
x^2 - 20x + 18 = 0

Now we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula.

After solving the quadratic equation, we find that the solutions are x = 18 and x = 1. However, we are only interested in positive values for x, so the final solution is x = 18.

Therefore, Michael would take 18 hours to paint the building alone, and Jamie would take 18 - 2 = 16 hours to paint the building alone.