Final answer:
Kalid, Natnael, and Ali worked together to complete a task in a total of 6 days. Kalid worked alone for the first two days, then Natnael joined for another two days, and finally, Ali joined them for the remaining work.
Step-by-step explanation:
Kalid can complete work in 18 days, which means Kalid does 1/18 of the work in a day. Natnael and Ali can complete the same work in 12 days and 6 days respectively, meaning Natnael does 1/12 of the work in a day, and Ali does 1/6 of the work in a day. Let's calculate how much of the work is done each day and find out the total time taken.
Kalid worked alone for 2 days:
2 * (1/18) = 2/18 or 1/9 of the work done
Natnael joins Kalid for the next 2 days, so they together work for 1/18 + 1/12 of the work each day:
2 * (1/18 + 1/12) = 2 * (2/36 + 3/36) = 2 * (5/36) = 10/36 or 5/18 of the work done
When Ali joins, all three work together. Combined, they do 1/18 + 1/12 + 1/6 of the work in a day:
= (2+3+6)/36 = 11/36 of the work in a day
By this point, Kalid and Natnael have completed 1/9 + 5/18 = 2/18 + 5/18 = 7/18 of the work. So, there is 11/18 of the work left to be done by all three.
To calculate how many days they need to finish the remaining work, we do:
11/18 divided by 11/36 = 11/18 * 36/11 = 2 days
Adding all the days up, we have:
2 days (Kalid) + 2 days (Kalid + Natnael) + 2 days (Kalid + Natnael + Ali) = 6 days in total
The work was completed in 6 days.