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Rate Word Problems - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To solve rate word problems, knowledge of solving systems of equations is necessary. Rate word problems include problems dealing with rates, distances, time and wind or water current. Other types of word problems using systems of equations include money word problems and age word problems.

Alright guys some of the most scary Math problems that you see in your Algebra classes have to do with rates, distances and time. It's like things traveling and they come in word problems which makes them scary to begin with and then also a lot of times people joke about these problems you know you see like the train leave Pittsburgh and the other train leaves New York and what time is it in Hawaii or whatever. They all use like really, they look like they're scary tricky problems that have to do with how fast things are traveling and for how long.
We're going to be looking at those types of problems and they're really scary but you guys the thing you want to remember is this one formula. Distance equals rate times time some people will call this the dirt formula like distance equals dert it's not kind of funny, not really mass joke. So this is the thing you want to keep in mind, you can also rearrange this like sometimes you wanted the rate all by itself you could dived both sides by time and sometimes you might see this formula written like this it's the same thing just rewritten. This is the one most important formula you're going to be using for these problems.
The other thing you'll have to keep in mind when you see these problems, is what's constant for both of the moving things and what's different. Like maybe they both move the same amount of time. Or maybe they both travel the same distance but different speeds and times that they're traveling, things like that. Keep in mind what's the same for both of your 2 different moving items.
The other thing that you want to think about is a lot of times you see problems that have to do with air speed or current so if you have a plane that's traveling, I have a little plane I want to show you. You have a little plane that's flying through the air with the wind right? The wind is going to make it go faster, instead of going like this if the wind is pushing it it's going to go woosh woosh a lot faster. And your formula for rate is going to involve rate plus wind speed, as opposed to if this airplane's flying into the wind and your rate quantity here you're going to be using how fast the plane is going take away that wind speed. The wind is going to slow it down, here it comes plane hits the wind slower that's going to affect the rate in this problem. So again guys when you're doing these problems this is the formula you're going to use if it involves air speed or water currents speed it's going to have like a change in your r quantity here. But the most important thing is to keep in mind what's the same for both of your moving airplanes or moving boats or whatever.

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