It takes Sisyphus two days to carry a pile of rocks up a hill. When I helped out, it took us only 1.2 days to carry all of the rocks. How long would it take me to carry the rocks by myself?
rates add:
books/1.2=books/my time + books/2days
multiply both sides by
my time*1.2*2/books
2*mytime=1.2*2+mytime*1.2
mytime(2-1.2)=2.4
my time=3days
1/2 + 1/x=1/1.2
1.2x+2.4=2x
.8x=2.4
x=3 days working by yourself. ☺☺☺☺
To determine how long it would take you to carry the rocks by yourself, we need to understand how much work each person is doing and how their individual efforts are affecting the total time.
Let's start by figuring out how much work Sisyphus does in two days. Since it takes him two days to carry the rocks up the hill, we can say that he does half of the work. This means that he carries half of the rocks up the hill in two days.
When you help out, the two of you manage to complete the remaining half of the work in 1.2 days. Since both of you are working, we can divide the work between the two days equally. Therefore, each day, together, you both complete 1/2 of the remaining work.
Now, to determine how much work you alone can do in one day, we subtract Sisyphus' work from the total work done in a day when you both are helping out. Mathematically, we can express this as:
1 day's work with both of you - 1 day's work of Sisyphus = 1 day's work done by you
Since Sisyphus completes half of the work in two days, we can say that his one day's work is 1/2 of the remaining work. Hence:
1 day's work with both of you - 1/2 day's work of Sisyphus = 1 day's work done by you
Now, let's substitute the given values:
1 day's work with both of you - 1/2 day's work of Sisyphus = 1 day's work done by you
1/2 - 1/2 = 1 day's work done by you
0 = 1 day's work done by you
This equation implies that you complete no work alone in one day because the result is zero. Therefore, carrying the rocks by yourself would take an infinite amount of time since you do not contribute any work towards finishing the task.