Lesson 17
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.
 20 gallons per hour
 10 feet per minute
 0.1 kilograms per second
Problem 2
A bank charges a service fee of $7.50 per month for a checking account.
A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?
Problem 3
A submarine is searching for underwater features. It is accompanied by a small aircraft and an underwater robotic vehicle.
At one time the aircraft is 200 m above the surface, the submarine is 55 m below the surface, and the underwater robotic vehicle is 227 m below the surface.
 What is the difference in height between the submarine and the aircraft?

What is the distance between the underwater robotic vehicle and the submarine?
Problem 4
Evaluate each expression. When the answer is not a whole number, write your answer as a fraction.
 \(\text4 \boldcdot \text6\)
 \(\text24 \boldcdot \frac {\text{}7}{6}\)
 \(4 \div \text6\)
 \(\frac43 \div \text24\)
Problem 5
 A restaurant bill is $21. You leave a 15% tip. How much do you pay including the tip?

Which of the following represents the amount a customer pays including the tip of 15% if the bill was \(b\) dollars? Select all that apply.
 \(15b\)
 \(b+0.15b\)
 \(1.15b\)
 \(1.015b\)
 \(b+\frac{15}{100}b\)
 \(b+0.15\)
 \(0.15b\)
Problem 6
Consider a rectangular prism with length 4 and width and height \(d\).
 Find an expression for the volume of the prism in terms of \(d\).

Compute the volume of the prism when \(d=1\), when \(d=2\), and when \(d=\frac12\).