A man can do the job in 8 days after 3 days of working a new guy help him and it takes 3 more days to finish the job together. how long will it take the new guy to finish the job alone?
After 3 days, there is still 5/8 job left to do.
(5/8)/3 = 1/8 + 1/x
x = 12
Check:
In 3 days, the man can do 3/8 of the work
The helper can do 3/12 = 1/4 of the work
3/8 + 1/4 = 5/8, the amount of the work left to do.
To find out how long it will take the new guy to finish the job alone, we can break down the information given in the question and calculate it.
Let's consider the work done by the man in one day as "M" and the work done by the new guy in one day as "N."
From the information given, we know that the man can complete the job in 8 days. Therefore, in one day, the man completes 1/8th of the job, which can be represented as:
1/8th of the job = M
After working for 3 days, the man and the new guy complete 3/8th of the job together, which can be represented as:
3/8th of the job = (M + N) * 3
We also know that when they work together for a total of 6 days (the initial 3 days by the man and the additional 3 days together), they complete the entire job, which can be represented as:
1 job = (M * 3) + (M + N) * 3
We can rearrange the above equation to solve for N (the work done by the new guy in one day):
1 job = 3M + 3M + 3N
1 job = 6M + 3N
As we already know that the man completes 1/8th of the job in one day (M = 1/8), we can substitute this value into the equation and simplify it further:
1 job = 6 * (1/8) + 3N
1 job = 3/4 + 3N
Since both sides of the equation represent the same job, we can equate them and solve for N:
3/4 + 3N = 1
3N = 1 - 3/4
3N = 4/4 - 3/4
3N = 1/4
N = 1/12
Therefore, the new guy can complete 1/12th of the job in one day. Now, to find out how long it will take him to complete the entire job alone, we can calculate it as:
1 job = (1/12) * X
Simplifying the equation, we get:
1 = X/12
X = 12
Hence, it will take the new guy 12 days to complete the job alone.