Math Problem, Need help urgently Please!?

Work = Rate * Time Work here is just "1", since it's undefined quantitatively, and will be "1" through the whole problem. You are told that A and B takes 18 days to complete the work when working together. So the rate of "A" (which I'll call "a") gets added to the rate of "B" (called "b") for the total rate: r = a + be So we have: w = rt 1 = (a + b)(18) 1 = 18a + 18b Then we are told that A leaves after 10 days, then B finished on his own.

So we need to find out how much of the job has been done in that 10 days: w = rt w = (a + b)10 w = 10a + 10b So whatever "w" is, there is (1 - w) work left that "B" finishes on his own in 12 days: w = rt.

When A leaves the job, the job is 5/9 finished, so B takes 12 days to do 4/9 of the job, which means B does 1/27 of the job per day. In 18 days, B does 18/27 = 2/3 of the job, so A does 1/3 of the job in 18 days. If A works alone, it would take him/her 54 days to do the whole job.

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