Week 16-Story Problems with Rational Expressions

Once you know how to solve rational equations, you will be ready for story problems. The method of solving these problems will be the same with the basic rational equations, however the challenge here is locating the information and organizing it in a way that allows you to solve the problem. For example:

A Boat travels 5Km upstream in the same amount of time it travels 12Km downstream. The average speed of the current is 4Km/h. What is the average speed of the boat in still water?

The relevant information that we need is distance, both downstream and upstream, and speed. Time is negligible because we already know that it is the same. Our distance downstream is 12, our distance upstream is 5. Our current downstream is 4, and upstream is -4. So now we can write it out as an equation:

12/x+4 = 5/x-4. x ≠-4, and 4. when you cross multiply, you get 12x-48 = 5x+20 and it’s a normal equation at this point, so just isolate the variable like you would normally do:

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