Question

It takes a painter and his friend 8 hours to paint a room. If the painter was working alone, it would take him 12 hours less than if his friend was working alone. How long does it take the painter to paint the room by himself?

Answer 1

It takes the painter 16 hours to paint the room by himself.

Step-by-step explanation:

Let's assume that the painter's friend can paint the room in x hours. According to the given information, the painter alone would take 12 hours less than his friend to complete the task. Therefore, the painter would take (x - 12) hours to paint the room alone.

When the painter and his friend work together, they can complete the task in 8 hours. We can express this information using the formula:

1 / (x - 12) + 1 / x = 1 / 8

To solve this equation, we multiply through by 8x(x - 12) to eliminate the fractions:

8(x - 12) + 8x = x(x - 12)

Simplifying further, we get:

16x - 96 = x² - 12x

Rearranging the equation and solving for x, we find:

x² - 28x + 96 = 0

Using the quadratic formula, x = 16 or x = 6. As the painter's friend cannot paint the room in less time than the painter, we discard the solution x = 6. Therefore, it takes the painter 16 hours to paint the room alone.