Answer:
It would take Tom 8 hours alone
Step-by-step explanation:
We are looking at this basic equation:
Tom + Shirley = 8 hours
Tom takes x hours to cut the grass; this means that 1/x of the job gets done in 1 hour
It takes Shirley 3 times as long as Tom, so it takes her 3x hours to cut the grass; this means that 1/3x of the job gets done in 1 hour
If the total number of hours it takes them to do the job is 6 hours; this means that 1/6 of the job gets done in 1 hour
Looking back at the original basic equation, we will fill in our info:
[tex]\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}[/tex]
We can solve for x by first finding the LCD and eliminating the denominators. The LCD is 6x, since all the denominators go into 6x evenly.
We will multiply the rational equation through by the LCD:
[tex]6x[\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}][/tex]
Dividing each denominator into the LCD gives us:
6 + 2 = x so
x = 8
This means that it takes Tom 8 hours to do the job alone. It would take Shirley 24 hours alone. Ugh.
