Exercise 27 Page 739

We are told that Lee can shovel a driveway in $3$ hours and Susan can do it in $2$ hours. We will find the time $t$ that it would take for them to do the job together. Let's start by finding the unit rate of the portion of the driveway per hour that can be completed by Lee and Susan, individually. Note that the product of rate and time gives the fraction of the job done. We can multiply each rate by the time $t$ to represent the amount of the job done by each person.

People	Rate ($\text{driveway}/\text{hour}$)	Fraction of the Job Done
Lee	$\frac{1}{3}$	$\frac{1}{3}t$
Susan	$\frac{1}{2}$	$\frac{1}{2}t$

The sum of the fractions that represent the amount of the job done by each person will be equal to $1.$ We will solve this equation by multiplying both sides by the least common denominator (LCD). It would take them $\frac{6}{5}$ hours to shovel the driveway together, which corresponds to option J.