Exercise 1 Page 588

We are told that Greg's father can mow the lawn on his riding mower in $45$ minutes. Dividing $1$ lawn by $45$ minutes, we can find the speed of Greg's father, or what part of the lawn he is mowing during one minute. Similarly, we can calculate Greg's speed knowing that it takes him $1$ hour $45$ minutes, or $60+45=106$ minutes to mow the lawn with a push mower. Adding these speeds, we can find their speed of mowing when working together. This expression tells us what part of the lawn Greg and his father can mow in one minute. How can we find the number of minutes $t$ it would take them to mow the entire lawn working together? Since the part of the lawn done varies directly as the time Greg and his father worked, we can set up the following proportion. Dividing a number by $1$ always results in the same number, so we can simplify the left-hand side of the equation by writing $\frac{1}{45}+\frac{1}{105}$ instead of the fraction. We will also multiply both sides of the equation by $t$ to get rid of the fraction of the right-hand side. The answer is C.