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# algebra

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Anthony and Billy can built a wall in 6 days, Billy and Corey can do it in 9 days and Corey and Anthony in 12 days.  How many days will it take the three of them together to build the wall?

Oct 15, 2020

#1
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Let's see how long it wil take them to build THREE walls....then divide the resulting time by 3

1/6  + 1/9  + 1/12  =  3/x

(12 + 8 + 6) / 72  = 3/x

26/72 = 3/x

x = 3 * 72/26    x = 8.30769   for THREE walls

One wall = 2.7692 days

Oct 15, 2020
#2
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EP, your solution method will not give the correct result. The performance times (contributions) of an individual worker is combined (buried) with the times of two (2) other individual workers. These individual times have to be extracted (separated) from the data before they are recombined for a collective result.

Note that by doubling your result, the time will then be very close to the correct calculated time. This is because the times used in your calculation are based on two workers.

--. .-

Oct 15, 2020
#3
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Oct 15, 2020
#4
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*** UPDATE ***     My answer above is incorrect....

1/(A+B) = 6                         1/(B+C) = 9                     1/(C+A) = 12

B = (1-6A)/6                                                                  C = (1-12A)/12

1/ [ (1-6A)/6 + (1-12A)/12]

Solve for   A = 15/216

then       B= 21/216

and        C = 4/216

1/(A+B+C) = x

1/(40/216) = x

216/40 = x = 5.4 days                    (IF I did all of the calcs w/out error!!)

Oct 15, 2020
edited by ElectricPavlov  Oct 15, 2020