# 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?

##### 1 Answer

The ycan finish the task in

#### 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 **one day**.

#underbrace(1/24 + 1/24 + ... + 1/24)_(color(blue)("24 days")) = 24/24 = 1#

Likewise, Andrei can complete *the same* task in **18 days**, which means that he can complete **one day**.

#underbrace(1/18 + 1/18 + ... + 1/18)_(color(blue)("18 days")) = 18/18 = 1#

This means that **together** can they finish

#1/24 + 1/18 = (18 + 24)/(24 * 18) = 42/432 = 7/72#

of a complete task in one day.

Therefore, to complete the task, they will require

#7/72 * "x days" = 1 implies x = 72/7 = 10 2/7 "days"#