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Question 92252: Bob can do a job in 1 hour, John can do the same job in 2 hours, Lisa can do the same job in 3 hours. How long would the job take if they all work together?
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Hi,
Well, we know that it will definitely take less than an hour (because Bob can do it in an hour) so let's work with minutes. What we want to consider is what fraction of the job can be done in a minute.
Now, Bob can do the job in 60 minutes, so in 1 minute, Bob does 1/60th of the job. It takes John 120 minutes, so in 1 minute, John can do 1/120th of the work. Similarly in a minute, Lisa can do 1/180th of the work.
So that means tat the amount of work that gets done in a minute is (1/60 + 1/120 + 1/180 = 11/360).
Now we know how much that gets done per minute, but we want to know how many minutes it takes to do the whole lot (the whole lot is 1). So 1/(11/360)=360/11 which on my calculator is just under 33 minutes.
For any problem like this, work out how much happens per minute(or hour or year or whatever) then see how long it it would take to do the whole lot.
Kev
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