# Rates

The Industrial Revolution is well-known as a time of explosive economic growth and invention. Here are five top inventions--and why they're important! Any of them would make a noteworthy Excellent Example in your SAT essay.

## 4/6 Rates

Always stop and read carefully before you do anything else. Make sure that you mark the bottom line and carefully label each step of your scratch work. It's easy to let confidence trick you into thinking it's safe to skip steps, but on a high-stakes test like the SAT, writing down each step and making sure that every answer is right can be the difference between acceptance and rejection at the school of your dreams. Once you find an answer, loop back to make sure that you have answered what the question asked. Then, and only then, should you select your answer from among the answer choices.

A machine can insert letters in envelopes at the rate of 120 per minute. Another machine can stamp the envelopes at the rate of 3 per second. How many stamping machines are needed to keep up with 18 inserting machines of this kind?

When you read this question carefully, one thing that should jump out at you is the fact that you have two different units of measurement. Immediately think, "I could convert both of these to seconds." Look for the bottom line: How many stamping machines do you need?

s = ?

Next, focus on your options. What could I do? What should I do? You could, as previously mentioned, convert one rate so that they use the same unit of measurement. But what could you do after that? You could guess, if you feel that this problem is too hard and that your time is better spent elsewhere, but guessing is only allowed on the test. No guessing during practice! The next option is to write an equation to describe what is happening in this problem, and then solve for s.

Let's start by converting the inserting machine's rate into seconds.

i: 120/60 = 2

Each inserting machine can stuff 2 envelopes per second.

Next, set up a formula to compare the number of envelopes that the machines can prepare. Each inserter can stuff 2 envelopes each second, and each stamper can stamp 3 envelopes per second. Plug the 18 inserting machines n for i.

2i = 3s

2(18) = 3s

Now solve for s.

$\frac{2(18)}{3}=s$

2(6) = s

12 = s

Loop back to make sure that what you found was the correct answer. s represents the number of stamping machines needed to prepare an equal number of envelopes as i inserting machines. Each inserting machine completes 2 envelopes per second, while each stamping machine finishes 3. Logically, you need fewer stamping machines than inserting machines. Look at the answer choices:

A) 12

B) 16

C) 20

D) 22

E) 24