This week in math, we learned how to solve word problems using rational equations. There are four different types of word problems; proportion, work, motion and distance, speed and time. To solve any of these, we must read over the problem carefully and find any clues that would lead to the creation of an equation.
The style of word problem that I found the most difficult were word problems involving work. Here’s an example:
The first thing that we to do is go through and highlight all the pertinent information.
Then we can make a table to collect all our information and make it easier to create an equation:
The time represents hours. Jenny represents a fraction out of five for each hour because it will take her 5 hours to finish. Jenny’s son represents a fraction out of x because we don’t know how long it will take him to finish. In the “together” column, we can put a 1 to represent that they have finished after three hours because we know that is how long it will take both of them. Our equation is 3/5 + 3/x = 1 because Jenny’s fraction and Jenny’s Son’s fraction will equal to one.
Now, we can use algebra to solve for x:
X = 7.5 but we can put the x value back into the equation to check our answer.
Since we have found out x value, we know that it would take Jenny’s son 7.5 hours to clean out the garage on his own.