during two hours at one area high school there are 3 class changes and two class periods. if the time spent in class is six less than six times the time spent changing classes, how long are the classes at this high school?
length of class change --- x
length of each class--- y
but y = 6x - 6
3x + 2y = 120
3x + 2(6x-6) = 120
3x + 12x - 12 = 120
15x = 132
x = 8.8
y = 46.8
To find out how long the classes are at this high school, let's break down the information given in the question step by step.
Step 1: Identify the components of the time frame:
There are two class periods and three class changes during a span of two hours.
Step 2: Set up equations based on the given conditions:
Let's assume the time spent changing classes as 'x' (in minutes).
Since there are three class changes in two hours, the total time spent changing classes would be 3x minutes.
The time spent in class is six less than six times the time spent changing classes, so the total time spent in class would be 6x - 6 minutes.
Since there are two class periods in two hours, the average time for each class period would be (6x - 6) / 2 minutes.
Step 3: Solve for 'x':
Since the question asks for the length of the classes at this high school, we need to solve for 'x' to find that out.
Given:
Total time spent changing classes = 3x minutes
Total time spent in class = 6x - 6 minutes
Total time frame = 2 hours = 120 minutes
Now let's set up the equation:
Total time spent changing classes + Total time spent in class = Total time frame
3x + 6x - 6 = 120
Combine like terms:
9x - 6 = 120
Add 6 to both sides:
9x = 126
Divide both sides by 9:
x = 14
Step 4: Calculate the length of the classes:
Now that we know x = 14, we can substitute it into the expression (6x - 6) / 2 to find the length of the classes at this high school.
Length of each class = (6x - 6) / 2
= (6 * 14 - 6) / 2
= (84 - 6) / 2
= 78 / 2
= 39 minutes
Therefore, the classes at this high school are 39 minutes long.