# Lesson 12

Negative Rates

Let's apply what we know about signed numbers.

### Problem 1

Describe a situation where each of the following quantities might be useful.

1. -20 gallons per hour
2. -10 feet per minute
3. -0.1 kilograms per second

### Problem 2

A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.

1. At what depth is it after:

1. 1 stage
2. 2 stages
3. 4 stages
2. How many stages will it take to return to the surface?

### Problem 3

Some boats were traveling up and down a river. A satellite recorded the movements of several boats.

1. A motor boat traveled -3.4 miles per hour for 0.75 hours. How far did it go?
2. A tugboat traveled -1.5 miles in 0.3 hours. What was its velocity?
3. What do you think that negative distances and velocities could mean in this situation?

### Problem 4

1. A cookie recipe uses 3 cups of flour to make 15 cookies. How many cookies can you make with this recipe with 4 cups of flour? (Assume you have enough of the other ingredients.)
2. A teacher uses 36 centimeters of tape to hang up 9 student projects. At that rate, how much tape would the teacher need to hang up 10 student projects?
(From Unit 4, Lesson 3.)

### Problem 5

Evaluate each expression. When the answer is not a whole number, write your answer as a fraction.

1. $$\text-4 \boldcdot \text-6$$
2. $$\text-24 \boldcdot \frac {\text{-}7}{6}$$
3. $$4 \div \text-6$$
4. $$\frac43 \div \text-24$$
(From Unit 5, Lesson 11.)