The producer of a 30 minute tv documentary about world war 1 divided it into two parts. four times as much program time was devoted to the causes of the war as to the outcome. how long is each part of the documentary?
Let x = causes and y = outcome.
x = 4y
x + y = 30
Substitute 4y for x in the second equation and solve for y. Insert that value into the first equation to solve for x. Check by putting both values into the second equation.
To solve this problem, we need to set up a proportion based on the given information. Let's call the length of time devoted to the causes of the war "x" minutes. Since four times that amount of time is devoted to the outcome, the length of time devoted to the outcome is "4x" minutes.
According to the problem, the total length of the documentary is 30 minutes. Therefore, we can set up the following equation:
x + 4x = 30
Combining like terms:
5x = 30
To solve for "x," we divide both sides of the equation by 5:
x = 30 / 5
x = 6
So, the length of time devoted to the causes of the war is 6 minutes, and the length of time devoted to the outcome is 4 times that, which is:
4x = 4 * 6 = 24 minutes
Hence, each part of the documentary is 6 minutes and 24 minutes long, respectively.