A can do work alone in 15 days whereas B can destroy entire work in 20 days. They are working on alternate days with a working on the first day, B working on the second day, then how many days will work completed?
To determine how many days it will take for the work to be completed, we need to find the combined work done by A and B in one day.
Since A can complete the work in 15 days, their work rate per day is 1/15.
Similarly, B can destroy the entire work in 20 days, so their work rate per day is -1/20 (negative because they are destroying the work).
On alternate days, only one person works, so we can add their individual work rates to find the combined work rate per day:
Combined work rate per day = A's work rate per day + B's work rate per day
= 1/15 + (-1/20)
= 4/60 - 3/60
= 1/60
Therefore, the combined work rate per day is 1/60.
To find the number of days it will take to complete the work, we can take the reciprocal of the combined work rate per day:
Number of days to complete the work = 1 / (combined work rate per day)
= 1 / (1/60)
= 60 / 1
= 60 days
Therefore, it will take 60 days for the work to be completed.
To find out how many days it will take for the work to be completed, we need to calculate the combined work rate of A and B.
Let's first calculate their individual work rates:
- A can complete the work in 15 days, so their work rate is 1/15 per day.
- B can destroy the work in 20 days, which means their work rate is -1/20 per day (negative because they are destroying the work).
Since A and B are working on alternate days, we can consider one cycle as A working on Day 1 and B working on Day 2. In each cycle, they contribute the sum of their individual work rates:
- A's work rate: 1/15 per day
- B's work rate: -1/20 per day
To find the combined work rate per cycle, we add their individual work rates:
1/15 + (-1/20) = (4/60) + (-3/60) = 1/60 per cycle.
Since they are working on alternate days, we can assume that the work rate remains constant throughout. Therefore, in each pair of days (one cycle), they complete (or destroy) 1/60th of the work.
To determine the number of days it will take for the work to be completed, we divide the total work (1 whole unit) by the work done per cycle (1/60):
1 / (1/60) = 60
Therefore, it will take 60 cycles, which corresponds to 60 days (since each cycle consists of two days), to complete the work.
A does 4/60 and B undoes 3/60
so 1/60 completed every 2 days
after 112 days, 56/60 are done
... A completes the work on the 113th