Week 16 – Pre Calc 11

This week in Pre-Calculus 11 we finished the Rational Expressions unit. This week we learned about the application of rational equations in real life situations.

Word Problem Basics: Word problems always contain valuable information for solving the problem, so it is always useful to read the question slowly and carefully. To understand the problem better you can create a chart or organize the information in a format you like. Being able to identify key words like greater than (+), less than (-), the sum (x+x), the difference (x-x), the quotient (), the product of (), etc. These words are helpful to remember when solving a word problem. When giving the answer to a word problem always answer with a sentence and with the units.

Ex. Sally can do all the house’s chores in 55 minutes. When Sally and Jake work together, they can do all the chores in 32 minutes. How long does it take Jake to do the chores?

What We Know: 

From the clues in the word problem we know the time it takes Sally to do all the chores and how long it takes Jake and Sally together to do all the chores. Because they complete all of the chores in that amount of time we know that they complete 100% of the chores, which can be represented as .

The Equation:

The first fraction represents the portion which it takes Sally and Jake to do all the chores over the amount of time Sally takes by herself. The second fraction represents the amount of time Sally and Jake take to do all the chores over the time Jake can do the chores. The time that Jake takes to do the chores is represented by because we are solving for that variable. The sum of both the rational numbers is because they complete all of the chores.

Solving:

 

Final Answer: It takes Jake around 76.5 minutes to do all the chores by himself.