Algebra: Chapter 10-7, p 455
Using Rational Equations
We are working on DRT problems and “WORK” 1/x problems. These say, if it takes one person 2 hours to do a job and another person 3 hours, how long does it take them both, working together to do the job.
Here is a link for DRT problems and here is a link for these work type of problems.
Remember, for the work problems, think of setting up the problem on a per hour basis. For example, if it takes one person `3` hours to paint a wall and another `5` hours, then in 1 hour, each person can do `1/3` and `1/5` of the project. If you put them together, then it would take `t` time, BUT, if you only worry about 1 hours’ worth with both working together, then in 1 hour they can both do `1/t` of the project.
Adding this up, we would get an equation that looks like:
`1/3` + `1/5` = `1/t`.
You know how to solve that by first finding the LCM (in this example it is `3*5*t` or `15t`)
Math-8, Chapter 10-5, p 509
Counting
The Fundamental Counting Principle: If event `M` can occur in `m` ways and is followed by event `N` that can occur in `n` ways, then the event `M` followed by event `N` can occur in `m * n` ways.
Sometimes, it is easy to draw a TREE diagram, like that pictured on page 509 of the textbook. Tree diagrams shows all the possible choices or outcomes. A good example problem is that one shown on page 509 – the problem about the bakery that offeres chicken, tuna and vegetable sandwiches on plain or onion bagels.