# Mark can finish task alone in 24days while Andrei can do the same task in 18days. If they work together, how long can they finish the task?

Sep 8, 2015

The ycan finish the task in $\frac{72}{7} \text{days}$.

#### Explanation:

The key here is to find out how much work can Mark and Andrei do per day.

This way you can figure out how much work they can do together in one day.

So, Mark can complete the task in 24 days, which means that he can complete $\frac{1}{24}$ of the task in one day.

${\underbrace{\frac{1}{24} + \frac{1}{24} + \ldots + \frac{1}{24}}}_{\textcolor{b l u e}{\text{24 days}}} = \frac{24}{24} = 1$

Likewise, Andrei can complete the same task in 18 days, which means that he can complete $\frac{1}{18}$ of the task in one day.

${\underbrace{\frac{1}{18} + \frac{1}{18} + \ldots + \frac{1}{18}}}_{\textcolor{b l u e}{\text{18 days}}} = \frac{18}{18} = 1$

This means that together can they finish

$\frac{1}{24} + \frac{1}{18} = \frac{18 + 24}{24 \cdot 18} = \frac{42}{432} = \frac{7}{72}$

of a complete task in one day.

Therefore, to complete the task, they will require

$\frac{7}{72} \cdot \text{x days" = 1 implies x = 72/7 = 10 2/7 "days}$