hey, I made a formula for some of the more complex rate problems for the practice portion on algebra 1. I know that what you're supposed to do anyways, but I just thought I'd share because it's a lot of fun. It's also interesting to see how many applications there are. It seems that when given a scenario you're often given variables with larger quantities, I think it always helps to see what those variables might be in a more simplified form. For example, here's a practice question from khan academy: 

It takes 36 minutes for 7 people to paint 4 walls. How many minutes does it take 9 people to paint 7 walls?

To answer this, you need to figure out how long it takes for 1person to paint 1 wall. So I used this formula:  a= b * 1/x(y)      
[a=time it takes for 1person to complete 1 wall.] [b=Time it takes for y/x. or, people per wall.] [x=the amount of walls] [y=the amount of people]
So, plugging in the variables...  a=36 * 1/4(7). This then gives you the answer a=63

Next, you need to simply plug that information into another formula. T=a/y(x)
[t=total amount of time] [a=time it takes for 1 person to complete 1 wall] [y=the amount of people] [x=the amount of walls] Still using the same variables, this is our plug-in:
T=36/9(7). That leaves us with T=49 minutes.
It's fun to see how a formula can have many applications with just a few tweaks relative to the scenario. Anybody else have a fun formula that you've made that you'd like to share??