Question

two painters are working together and can paint a house in 3 hours. One painter alone can paint the same house in 8 hours. How many hours would it take the second painter to paint the house by himself

Answer 1

For this case, the first thing we must do is define a variable.
 We have then:
 x: number of hours it takes the second painter to paint the house working alone.
 We have then that the equation that models the problem is:
 $\frac{1}{x} + \frac{1}{8} = \frac{1}{3}$
 From here, we clear the value of x.
 We have then:
 $\frac{8x}{x} + \frac{8x}{8} = \frac{8x}{3}$
 $8 + x = \frac{8x}{3}$
 $24 + 3x = 8x$
 $24 = 8x-3x 24 = 5x$
 $x = \frac{24}{5}$
 $x = 4.8$
 Answer:
 It would take the second painter to paint the house by himself about 4.8 hours.