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
To find out how long it would take for B to do the work alone, we need to determine how much work A and B can do in a single day.
Given that A does 8/15 of the work in 8 days, we can calculate A's daily work rate by dividing the total work done (8/15) by the number of days (8):
A's daily work rate = (8/15) / 8 = 1/15
Now, let's find out how much work both A and B can do together in a single day. We know that they can complete the remaining work in 4 days, so the combined daily work rate of A and B is 1/4.
Since A's daily work rate is 1/15, we can subtract that from the combined daily work rate to find B's daily work rate:
B's daily work rate = Combined daily work rate - A's daily work rate = 1/4 - 1/15
To simplify the calculation, we need a common denominator for both fractions. The least common denominator (LCD) for 4 and 15 is 60. Let's rewrite the equation with the common denominator:
B's daily work rate = (15/60) - (4/60) = 11/60
Now, we know B's daily work rate is 11/60. To determine how long B will take to do the work alone, we need to calculate the reciprocal of the daily work rate:
Time for B to complete the work alone = 1 / (B's daily work rate) = 1 / (11/60) = 60/11
So, B will take approximately 5.45 (rounded to two decimal places) or 60/11 days to do the work alone.