Answer:
Given:
Painter A= 12 hours (Means he can do \frac{1}{12}121 job a day)
Painter B= 8 hours (Means he can do \frac{1}{8}81 job a day)
Painter A + Painter B= 1 job (Rate together is equal to \frac{1}{x}x1 )
Solution:
\frac{1}{12} + \frac{1}{8} = \frac{1}{x}121+81=x1
Multiply then by 24x to simplify the equation
2x+3x=24
5x=24
x=\frac{24}{5}524
Therefore, they can complete the job together in 4 hours and 48 minutes.
Checking:
Substitute the value of x to the original equation:
\frac{1}{12} + \frac{1}{8} = \frac{1}{x}121+81=x1
\frac{1}{8} + \frac{1}{12} = \frac{1}{ \frac{25}{4} }81+121=4251
\frac{2}{24} + \frac{3}{24} = \frac{5}{24}242+243=245
\frac{5}{24}= \frac{5}{24}245=245
