A does 8/15 of a work in 8 days and the remaining work is finished with the assistance of B in 4 days . how long will B take to do the work alone
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To solve this problem, we need to calculate the rate at which A and B work individually and then use that information to find B's time to complete the work alone.
Let's start by calculating A's rate. We know that A does 8/15 of the work in 8 days. To find A's daily work rate, we divide the fraction of the work A does by the number of days:
A's rate = (8/15) / 8 = 1/15 of the work per day
Next, we need to find the combined rate of A and B when they work together. Since A did 8/15 of the work in 8 days, we subtract that from 1 to find the remaining fraction of the work:
Remaining fraction of work = 1 - 8/15 = 7/15 of the work
We know that A and B together finish the remaining 7/15 of the work in 4 days. To find the combined rate of A and B per day, we divide the remaining fraction of work by the number of days:
Combined rate of A and B = (7/15) / 4 = 7/60 of the work per day
Now, we can find B's individual rate by subtracting A's rate from the combined rate of A and B:
B's rate = Combined rate of A and B - A's rate = (7/60) - (1/15) = (7/60) - (4/60) = 3/60 of the work per day
Since we know B's rate, we can determine how long it would take for B to complete the work alone by taking the reciprocal of B's rate:
B's time = 1 / (3/60) = 60/3 = 20 days
Therefore, it will take B 20 days to complete the work alone.