Can someone show me step by step on how to get the rate of something?

Question

Can someone show me step by step on how to get the rate of something?

Answer 1

Classic problem! A rate is a fraction, a division, of two things where each thing has separate meaning of the other, with one usually being time. For example: Miles/Hour, Fluid (Volume)/Sec, Energy/Time.

Now, here's the last thing needed to know: Rates require change. So that means you take two moments, subtract their respective values ("change") from each other (same order), and divide them. If something changes with time, we almost always divide by that change.

Equation form: (Y1-Y2)/(X1-X2), which is same as (Y2-Y1)/(X2-X1) because, notice the order?

If you subtract your first value (Y1 or X1) from your second (Y2 or X2), you must do the same on the other side, first from second.

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Practice problem 1: I went 8 miles in 4 hours. Rate? (in mph)

Here, they gave you the change! That means we just need to divide one from the other. Because one is a unit of time, we divide by that: 8/4=2 miles/hour (or miles per hour).

Practice problem 2: On day 3, I owe 50 dollars. On day 28, I own 100 dollars. My rate? (in dollars per day)

Keep in mind the difference between owing and owning (- vs +). Let's calculate the changes and then, as usual, divide by time. Change in money: (100 - (-50))=100+50=$150. This should make sense! You would have to gain $150 dollars in order to lose $50 of debt and have $100 left over. Change in time: (28-3)=25 days. Now the rate: 150/25=6 dollars per day!

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Ask questions as needed and realize that negative rates are possible, they just mean you're losing something. Make sure to subtract in the same order!