A company has a machine that can complete a job in 6 hours. With the help of a newer machine, the job can be completed in 2 hours. How long would the new machine take to do the job alone?

Question

jim_thompson5910 · Answer

$$\large \frac{1}{6}+\frac{1}{x}=\frac{1}{2}$$


$$\large \frac{x}{6x}+\frac{1}{x}=\frac{1}{2}$$


$$\large \frac{x}{6x}+\frac{6}{6x}=\frac{1}{2}$$


$$\large \frac{x+6}{6x}=\frac{1}{2}$$


$$\large 2(x+6)=6x$$


$$\large 2x+12=6x$$


$$\large 12=6x-2x$$


$$\large 12=4x$$


$$\large \frac{12}{4}=x$$


$$\large 3=x$$


$$\large x=3$$
So it would take 3 hours if the new machine was working alone.