Three workers

Three people - A, B, C . A and B can do a piece of work in 18 days, B and C can do it in 24 days, A and C can do it in 36 days.In how many days B alone can finish the work?

Correct answer:

B =  28.8

Step-by-step explanation:

a=1/A b = 1/B c = 1/C  18 (a+b)=1 24 (b+c)=1 36 (a+c)=1  18a+18b=1 24b+24c=1 36a+36c=1  Pivot:Row1Row3 36a+36c=1 24b+24c=1 18a+18b=1  Row33618 Row1Row3 36a+36c=1 24b+24c=1 18b18c=0.5  Row32418 Row2Row3 36a+36c=1 24b+24c=1 36c=0.25  c=360.25=0.00694444 b=24124c=24124 0.00694444=0.03472222 a=36136c=36136 0.00694444=0.02083333  a=4810.020833 b=14450.034722 c=14410.006944  A=1/a=1/0.0208=48 B=1/b=1/0.0347=5144=2854=28.8 C=1/c=1/0.0069=144



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Showing 1 comment:
Dr Math
Ahother steps:

A + B can do in 18 days ,
B + C can do it in 24 days ,
A + C can do it in 36 days.
A+B+C do/day = (1/18+1/24+1/36)/2 = (4+3+2)/72 = 1/16
B does/day = 1/16-1/36 = (9-4)/144 = 5/144
B can do in 144/5 = 28.8 days





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