Final answer:
Find how many days Adam, Biden, Carter, and Dwight will take to run a campaign together, we can use the formula for the combined rate of work. By setting up an equation and solving for the number of days, we find that the number of days required will depend on the value of y.
Step-by-step explanation:
Since Adam and Biden run a campaign together for 8 days, we can say that their combined rate of work is 1 campaign in 8 days.
Now, if we add Carter and Dwight to the team, we need to find the combined rate of work for all four of them. Let's assume that Carter and Dwight also complete a campaign in x days.
According to the work formula, Work = Rate x Time, we can set up the following equation:
1 / 8 + 1 / x = 1 / y
To solve for y, the number of days it will take for all four of them to run a campaign together, we can use the formula for the combined rate of work:
1 / y = 1 / 8 + 1 / x
To simplify the equation, we can find a common denominator:
1 / y = (x + 8) / 8x
Next, we can cross multiply:
8x = y(x + 8)
Expanding the equation:
8x = xy + 8y
We can now rearrange the equation:
xy - 8x = 8y
Factoring out the common factor:
x(y - 8) = 8y
Dividing both sides by (y - 8):
x = (8y) / (y - 8)
This equation gives us the number of days it will take for Carter and Dwight to complete a campaign together. Since there is no specific value given for y, we cannot determine an exact number of days. However, we can conclude that the number of days required will depend on the value of y.