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Rate Word Problems  Concept
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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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”
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Sample Problems (6)
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Rate Word Problems
Problem 1 9,761 viewsOne plane leaves New York City for LA going 500 mph. At the same time, a different plane leaves LA for New York City going 650 mph.
If the 2 cities are approximately 3000 miles apart; how far from LA are when they cross? 
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Problem 2 6,436 viewsA boat traveled 288 miles each way downstream and back. The trip downstream with the water current took 12 hours. The trip upstream against the current took 36 hours.
How fast would the boat be traveling in still water? How fast is the current? 
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Problem 3 4,869 viewsTo keep in shape, Alison walks a 12 mile course at a constant speed. If she doubles her usual speed, she can complete the course in 1½ hours less than her usual speed.
What is Alison's usual speed? 
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Problem 4 225 views 
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Problem 5 186 views 
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Problem 6 202 views
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Dr Neena Joshi · 1 month ago
I am Dr Neena Joshi, a Ph.D in MAthematics I just happened to see this site. It is very good and useful to the students. Congratulations for creating such a nice site and for being helpful to the students. I downloaded your Algebra book, just out of curiosity, hope you won't mind I have been writing many text books on Mathematics for year 11 and 12 as well as Uni Students in India, I know it is a hard work, Also, I liked the way Alissa was explaining rate word problems. She was making the concept interesting and easy to understand. I do not mind, if I can be of some help to you, and contribute in the noble cause of helping the students. Thanks and Warm regards neena