SOLUTION: A can do a work in 12 days and B in 18 days. A started the work and B joined him later. Find when did B join A, if the entire work is completed in 8 days?

Question 876671: A can do a work in 12 days and B in 18 days. A started the work and B joined him later. Find when did B join A, if the entire work is completed in 8 days?
Found 2 solutions by ankor@dixie-net.com, LinnW:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A can do a work in 12 days and B in 18 days.
A started the work and B joined him later.
Find when did B join A, if the entire work is completed in 8 days?
:
let t = time worked before B joined A to finish the job
let the completed job = 1
:
+ = 1
multiply by 36 to clear the denominators
3(8) + 2(8-t) = 36
24 + 16 - 2t = 36
40 - 2t = 36
-2t = 36-40
-2t = -4
t = +2 days when B joined A to finish the job
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!

A has a rate of 1/12 work per day
B has a rate of 1/18 work per day
(1/12)(time) + (1/18)(time - B's delay) = 1 task
The time is 8 days
set x = B's delay
(1/12)(8) + (1/18)(8 - x) = 1
8/12 + 8/18 - (1/18)x = 1
2/3 + 4/9 - (1/18)x = 1
multiply each side by 18
18(2/3 + 4/9 - (1/18)x ) = 1* 18
36/3 + 72/9 - x = 18
12 + 8 - x = 18
20 - x = 18
add -20 to each side
-x = -2
x = 2
So B joins A 2 days after the start
Checking,
(1/12)(8 days) + (1/18)(6 days) ?= 1
8/12 + 6/18 ?= 1
2/3 + 1/3 = 1
So our answer is correct

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