A and B can finish a piece of work in 12days and 18days respectively. A begin to the work and they work alternately one at a time for one day each.The whole work will be completed in?
Help me plz show step thanks
A&B together can do 1/12 + 1/18 = 5/36 of the job in a day
So, it will take them 36/5 * 2 = 72/5 days. or 14 2/5 days
After 14 days, they have each worked 7 days, so
7 * 5/36 = 35/36 of the job is done.
On the 15th day A works 1/3 of a day to finish up the last 1/36 of the task.
To solve this problem, we need to calculate the work efficiency of both workers, A and B.
Let's assume A's work efficiency is X units per day, and B's work efficiency is Y units per day.
Given that A and B can finish the work in 12 days and 18 days respectively:
A's work efficiency: X * 12 = 1 (since they complete the work in 12 days)
B's work efficiency: Y * 18 = 1 (since they complete the work in 18 days)
Now, we know that they work alternately, one at a time for one day each. In one single day, the combined work efficiency of A and B is:
A + B = (1 day work efficiency)
On day 1, A completes their work, so the remaining work is (1 - X).
On day 2, B completes their work, so the remaining work is (1 - Y).
Since their work efficiency is in units per day, we can create the following equation:
(1 - X) + (1 - Y) = (1 day work efficiency)
Simplifying the equation:
2 - (X + Y) = (1 day work efficiency)
(X + Y) = 2 - (1 day work efficiency)
Substituting the values of X * 12 = 1 and Y * 18 = 1:
(1/12 + 1/18) = 2 - (1 day work efficiency)
(3/36 + 2/36) = 2 - (1 day work efficiency)
5/36 = 2 - (1 day work efficiency)
Now, we can rearrange the equation and solve for (1 day work efficiency):
(1 day work efficiency) = 2 - (5/36)
(1 day work efficiency) = (72/36) - (5/36)
(1 day work efficiency) = 67/36
Since the question asks for the time required to complete the whole work, we can determine that the whole work will be completed in:
(1 day work efficiency)^-1 = (36/67) days
Therefore, the whole work will be completed in approximately 0.537 days.
Please note that this is an approximation and the actual value may be slightly different due to rounding.