# Math Help - Calculating Work Done.

1. ## Calculating Work Done.

I am having difficulty with the following problem:
Mr.Boone can do a job in 10 days . A helper joins him after 3 days and together they work for 4 days to complete the task.How many days would it take the helper to do the task alone ?
Note : the ans is 13.33

I know the formula for time taken for two people when working together is
T = 1/ ( (1/x) + (1/y))
But i cant manage to compensate mr boon for the 3 days he worked on his own. How would i do that ??

2. ## Re: Calculating Work Done.

Originally Posted by MikeNoob
Mr.Boone can do a job in 10 days . A helper joins him after 3 days and together they work for 4 days to complete the task.How many days would it take the helper to do the task alone ?
Mr. Boone can do one job in ten days. So after 3 days, he has already done 3/10ths of the job. Working together, it takes 4 days to finish the remaining 7/10ths. So we subtract the two rates to find the helper's work rate:

$\frac{7/10\ \mathrm{jobs}}{4\ \mathrm{days}}-\frac{1\ \mathrm{job}}{10\ \mathrm{days}} = \frac7{40}-\frac4{40}=\frac{3\ \mathrm{jobs}}{40\ \mathrm{days}}$

So in one day, the helper can complete 3/40ths of a job. To find the number of days it would take to complete an entire job, take the reciprocal:

$1\ \mathrm{job}\cdot\frac{40\ \mathrm{days}}{3\ \mathrm{jobs}}=13.\overline{3}\ \mathrm{ days}$.

3. ## Re: Calculating Work Done.

Really great, very nicely solved by Reckoner, even i got agreed with solution. Thanks for solving this problem.