Question

Tom and Shirley, working together can mow the lawn in 6 hours working alone Shirley takes three times as long as Tom how long does it take Tom to mow the lawn alone

Answer 1

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:

$\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}$

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:

$6x[\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}]$

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.