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
A's rate = (8/15)W / 8 = W/15
let B's rate = W/x , where x is the time it would take B to do the job
combined rate = W/15+W/x = (Wx + 15W)/(15x)
then 4(Wx + 15W)/(15x) = (7/15)W
divide by W and expand
(4x + 60)/(15x) = 7/15
times 15
(4x+60)/x = 7
multiply by x
4x + 60 = 7x
x = 20
it would take B 20 days
To find out how long B will take to do the work alone, we need to first determine the rate at which A and B work together.
Since A does 8/15 of the work in 8 days, we can calculate A's daily work rate by dividing 8/15 by 8:
A's daily work rate = (8/15) / 8 = 1/15
We know that A and B together finish the remaining work in 4 days, so we can calculate their combined daily work rate by dividing the remaining work (7/15, which is the remaining fraction of work since A did 8/15) by 4:
Combined daily work rate of A and B = (7/15) / 4 = 7/60
Now, to determine B's daily work rate, we need to subtract A's daily work rate from the combined daily work rate of A and B:
B's daily work rate = Combined daily work rate of A and B - A's daily work rate
B's daily work rate = (7/60) - (1/15)
B's daily work rate = 7/60 - 4/60
B's daily work rate = 3/60
B's daily work rate = 1/20
Finally, to find out how long B will take to do the work alone, we can calculate the number of days based on B's daily work rate:
B's working days = 1 / (1/20)
B's working days = 20
Therefore, it will take B 20 days to do the work alone.
To solve this problem, we can first find out how much work A completes per day. Then, we can use that information to determine how much work A completes in 8 days.
Let's assume that A completes 'x' amount of work per day.
Since A completes 8/15th of the work in 8 days, we can set up the following equation:
(x * 8) = 8/15
To solve for x, we can divide both sides of the equation by 8:
x = (8/15) / 8
x = 1/15
So, A completes 1/15th of the work per day.
Now, we need to find out how much work A completes in 8 days:
Work completed by A = x * Number of days
Work completed by A = (1/15) * 8
Work completed by A = 8/15
Now, we know that A completes 8/15th of the work alone. Therefore, B completes the remaining 7/15th of the work.
Since the remaining work is finished in 4 days, we can set up the following equation:
(7/15) / 4 = 1/B
To solve for B, we can multiply both sides of the equation by 4:
7/15 = 1/B
To isolate B, we can take the reciprocal of both sides:
B = 15/7
Therefore, B takes 15/7 days to complete the work alone or approximately 2.14 days.