combined work Math
Started by joonkimdds
What are you trying to figure out. Work=Rate x Time
combined work, meaning how much time it takes when many people are working together.
Is the answer 55 minutes ???
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yes it is.
I was wondering why kaplan method didn't work.
Isn't it supposed to be (Time 1 x time2) / (Time1+time2)?
I did it the long way.....
So A does 1/5 of the work in an hour
B does 1/2 while C the go getter that he is does 1/2.5 --> 2/5 of the work
So in total, in 1 hour they do 11/10 of the work (hypothetically)
So how long to do the full job i.e. 10/10
Ratio & proportions
11/10:1::10/10:x --> x = 10/11 = 0.9 hours = 55 minutes
So A does 1/5 of the work in an hour
B does 1/2 while C the go getter that he is does 1/2.5 --> 2/5 of the work
So in total, in 1 hour they do 11/10 of the work (hypothetically)
So how long to do the full job i.e. 10/10
Ratio & proportions
11/10:1::10/10:x --> x = 10/11 = 0.9 hours = 55 minutes
whatever method works for you, that's good 🙂
But I thought I was supposed to use the formula.
For example, if it takes 12 hrs and 6 hrs then it's
12x6 / 18 = 4hrs.
But for some reason, it didn't work for this example. Maybe it only works for 2 ppl but not for 3 ppl.
But I thought I was supposed to use the formula.
For example, if it takes 12 hrs and 6 hrs then it's
12x6 / 18 = 4hrs.
But for some reason, it didn't work for this example. Maybe it only works for 2 ppl but not for 3 ppl.
You need to figure out what the rate is before you can do the problem and use the equation Work = Rate X Time. Combined time is what is unknown.
The rate for each work is (1/5), (1/2), (1/2.5)
Work=60 since 1 that's the combine work, and 60 minutes in an hour
60=[(2/10)+(5/10)+(4/10)]X
60=(11/10)X
(10/11)60=X
55=X
The rate for each work is (1/5), (1/2), (1/2.5)
Work=60 since 1 that's the combine work, and 60 minutes in an hour
60=[(2/10)+(5/10)+(4/10)]X
60=(11/10)X
(10/11)60=X
55=X
It works for 2 because: 1/A + 1/B = 1/T (T = total)
Thus B/AB + A/AB = 1/T
(A+B)/AB = 1/T
T = AB/(A+B)
For 3 people: 1/A + 1/B + 1/C = 1/T
BC/ABC + AC/ABC + AB/ABC = 1/T
(AB + AC + BC) / ABC = 1/T
T = ABC / (AB + AC + BC)
That's your problem. Your denominator is wrong.
With 5, 2, and 2.5 hours:
T = (5)(2)(2.5) / [(5)(2) + (5)(2.5) + (2)(2.5)]
T = 25 / 27.5
T = 50/55 = 10/11 hour (about 55 minutes)
Thus B/AB + A/AB = 1/T
(A+B)/AB = 1/T
T = AB/(A+B)
For 3 people: 1/A + 1/B + 1/C = 1/T
BC/ABC + AC/ABC + AB/ABC = 1/T
(AB + AC + BC) / ABC = 1/T
T = ABC / (AB + AC + BC)
That's your problem. Your denominator is wrong.
With 5, 2, and 2.5 hours:
T = (5)(2)(2.5) / [(5)(2) + (5)(2.5) + (2)(2.5)]
T = 25 / 27.5
T = 50/55 = 10/11 hour (about 55 minutes)
ha, you guys think too much... I just did:
(5/3)(2/3)(2.5/3) = 25/27 hr... pretty easy to guestimate it's around 55mins...
Edit: Each over 3 because they each contribute 1/3 to the total workload
(5/3)(2/3)(2.5/3) = 25/27 hr... pretty easy to guestimate it's around 55mins...
Edit: Each over 3 because they each contribute 1/3 to the total workload
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Too bad these numbers worked out well with your incorrect method. If you'll notice, your numerator is identical to the one I have listed. Your denominator, however, is not. The reason you got lucky is because (5)(2) + (5)(2.5) + (2)(2.5) just happens to be close to 27 (which you will ALWAYS get with your method).
Try your way with something else... let's say 9, 8, and 12 hours.
My way gives 864 / 276 = 3.13 hours.
Your way gives 864 / 27 = 32 hours.
I don't think it would take those 3 people 32 hours to do the job if any one of them could finish it in under 12 hours.
ha, I stand corrected. my bad. I workied it out and was thinking it was too easy haha. Guess that's what I get for trying to do math even though I haven't studied for it yet. Oh well. Thanks a bunch for the correction though 😀, otherwise I probably would've done it that way on the actual dat 😛
I think the way you did it and the way I did it are the same just worded differently.
Your way was fine. I just wanted to show him why the formula he used was not working.
This is a fancy way to write a "rate * time = distance" problem. Here the rate is calculated with the 2/10 + 4/10 + 5/10. The time is represented in hours by the "X". The distance is the other side of the equal sign. Normally he'd use a 1 because you want to complete 1 full job. In that case X would be in hours. What if you wanted X to be in minutes? You would multiply it by 60. So to skip the middle step, he just multiplied both sides by 60. Now there's a 60 on the left, and on the right we have X in minutes instead of hours.
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