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# Working together A and B can do a job in 6 days. B & C

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Working together A and B can do a job in 6 days. B & C [#permalink]  26 Sep 2005, 19:36
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Working together A and B can do a job in 6 days. B & C can do the same job in 10 days while C and A can do it in 7.5 days. How long will it take if all A, B,C work together to complete the job? How long will it take for A alone, B alone, C alone to complete the job?
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Is this question complete??

I was thinking may be there's something missing, the only way i seem to solve the problem is by assuming one of the values, if i assume A can do the same job in 10 days alone and rest of it seems solvable...
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This question is complete, no need to assume any value....
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1/A+1/B=1/6......(1)

1/B+1/C=1/10...(2)

1/A+1/C=1/7.5.... (3)

SUBTRACTING (1) AND (2) WE GET
1/A-1/C=15....(4)

ADDING 3 AND 4 WE GET
2*1/A=1/5 THEREFORE 1/A= 1/10

NOW PUTTING VALUES OF A WE GET

B=1/15 AND C=1/30 (ie, A TAKES 10 DAYS, B TAKES 15 AND C TAKES 30 DAYS)

ADDING THEM ALL UP WE GET 1/5 ie, it takes 5 days for A B C to finish the work working together.

please correct me if i'm wrong
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Re: PS: Work problem [#permalink]  26 Sep 2005, 23:31
gmacvik wrote:
Working together A and B can do a job in 6 days. B & C can do the same job in 10 days while C and A can do it in 7.5 days. How long will it take if all A, B,C work together to complete the job? How long will it take for A alone, B alone, C alone to complete the job?

A,B,C combine will complete the job in 3 4/7 days. From here you may calculate the individual compleion time
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ADDING THEM ALL UP WE GET 1/5 ie, it takes 5 days for A B C to finish the work working together.

please correct me if i'm wrong[/quote]

I get the same answer as you. A = 10, B = 15, c= 30
Adding all of them we get 2 (1/A + 1/B+1/c) = 1/6 + 1/0 + 1/7.5
=> 1/A + 1/B + 1/C = 180/900 = 1/5
Together they would take 5 days.
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thanks guys
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