### Section 6.7, continued

Last time, we completed one example of a word problem involving both rational expressions and the idea of work: work = rate * time. Let's add one more idea: suppose that you are filling a jug that has a leak in the bottom. You are then filling the jug, but the leak is "unfilling" the jug. So your task would be "1 jug filled", while the leak would be "-1 jug filled", since the leak is undoing the filling.

The idea is that it's possible for the two people/pumps/objects to be working against each other, so you will assign negative signs as appropriate to keep things straight. Let's look at an example.

#### Example 1:

Sean can clean the living room in a certain amount of time. It takes his toddler half an hour less than that to completely destroy the room. If the two of them start together in a perfectly neat living room, it takes a total of 6 hours for the room to become a complete shambles. How long does it take Sean to clean the room?

#### Example 2:

A group of students working late at night orders $24 worth of pizza from Little Caesarâ€™s. After the pizzas have arrived, one more student shows up and helps to eat them. If the cost per person decreases by $2 due to this new student, how many students were there originally, and how much were each of those students paying?

#### Example 3:

Adventures, Inc. has a $1500 group rate for an overnight kayak trip. For the last trip, five people failed to show, causing teh price per person to increase by $25. How many were originally scheduled for the trip?