Paint a Fence
it takes Chris three hours to paint a fence. it takes Zaux 6 hours to do the same job. How long would it take both of them together to finish the job?
-Knightmare
-Knightmare
Labels: SharedPuzzle
posted by Rajesh Lal at
5:39 PM
13 Comments:
Paint a fence:
Chris takes 3 hrs. to finish job
Zaux takes 6 hrs. to finish job
Chris painting rate = 1/3 fence/hr.
Zaux painting rate = 1/6 fence/hr.
Together they would paint 1/3 + 1/6 fence in 1 hr. = 1/2 fence
Thus in 2 hrs. the job would be completed.
yeah,u got her,Zaux.
i'll try finding harder ones.
Really you should include more data. You don't know their speed unless you know the kind and length of the fences. For example...
Chris takes 3 hours to paint a 30 foot fence..........10 feet per hour
Zaux takes 6 hours to paint a 60 foot fence...........10 feet per hour
...........................................Together = 20 foot per hour
A new job of 90 foot
fence............................
90 / 20 = 4.5 hours
PS.
I am not disagreeing with you, and you did say the "same" job, but I would include more info to make it harder.
More likely, Chris and Zaux would stop painting and start arguing about their respective rates of productivity.
One would walk off in a huff, leaving the other to finish the job alone.
1 hour and a half
Aw come on Wiz ... I sincerely doubt that Chris and I would argue about the rate of productivity.
However ... a heated discussion about who is consuming an unfair share of the foamy beverage we purchased ... well, that's a whole different story... heh heh.
Hi Ragknot. If the fence that Zaux and I were painting together was not the same type as the one for which productivity is known, then the problem would be insoluble. It may be that for a different type of fence, our relative and absolute prodcutivity rates would be different.
Assuming the question isn't a trick one, then you have to assume an identical fence. You also have to assume that we don't get in each others way, otherwise our individual productivity rates would be reduced.
It may also be that the temperature that the job was being done at had changed, or that it had started raining, or that one of us had been drinking heavily (again), or that some protestors (the anti fence painting army) were preventing us from doing the job, etc.
The unwritten convention when solving puzzle type problems, is to make simplifying assumptions. By all means explicitly state the assumptions that are used. But as I've commented previously, the list of assumptions could be come infinitely large. These puzzle problems are not real-world problems requiring enormous amoounts of efforts to define accurately.
Personally, I call the approach that I take "practical engineering".
Parkinson's Law states, "The amount of time it takes to perform a task is directly proportional to the amount of time allowed to perform the task."
For instance- Any employee who takes the day off work to perform several errands will take all day to complete those errands. An employee who chooses to perform the same tasks during his lunch-hour will likely complete all those same tasks in an hour.
One will rely on the other to perform a certain amount of the task the other previously performed so their rate of work will be exponentially slower.
Hence, Chris takes 3 hrs. to finish job and Zaux takes 6 hrs. to finish job so combined it will take them 9 hours to complete the painting of the fence.
That sounds more likely to me.
I've changed my mind ... am not going to paint. Rather, I will sit and drink beer and watch Chris paint.
You missed a spot, Chris!
Rats! I'll have to start again.
Chris and Zaux continue their argument . . .
Chris accuses Zaux of slacking.
Zaux accuses Chris of doing a poor job of painting to finish it quickly.
Each tips their paint over the other.
Result: Time to paint the fence = lost time, plus time to hire new painters and a professional mediator, plus x hours. Cost of painting the fence is at least triple original estimates.
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