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It takes 24 hours for machine A to finish a work. After A

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Senior Manager
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It takes 24 hours for machine A to finish a work. After A [#permalink]  10 May 2005, 19:40
It takes 24 hours for machine A to finish a work. After A worked for 8 hours, the other part is to be finished by B, whose rate is 2/3 that of A. How much time will B take to finish the job?
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I may have read the question wrongly, so please let me know.

24/36 = 16/x

24x = 576

x = 24
VP
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24

24-8 = 16

16 = 2/3 B

B = 48/2 = 24
VP
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24...

A takes 24 h and B takes 36 h

8/24+x/36=1

x=24
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Rate : A - 1/24 ; B - (2/3)*(1/24)

After 8 hours 8/24 of the work is finished and 16/24 of the work is left which has to be completed by B

time = work/rate = (16/24)/ (2/24*3) = 24

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Re: work [#permalink]  11 May 2005, 18:42
Another way to look at this - use ratios:

rate of work for B = 2/3 A

Work left is also 2/3 A (i.e. 16/24 ).

So, using ratios, 2/3 (work left is directly proportional) and 3/2 (rate of work is inversely proportional) cancel out, leaving 24.

If it is confusing, see below...

Work Unit (to be finished) ---- Rate of Work------ Time to finish

A 1---------------------------------1----------------------24
B 2/3--------------------------------2/3-------------------X

Here X = 24 * 2/3 * 1/(2/3) = 24.

-Srinivas.

pb_india wrote:
It takes 24 hours for machine A to finish a work. After A worked for 8 hours, the other part is to be finished by B, whose rate is 2/3 that of A. How much time will B take to finish the job?
Re: work   [#permalink] 11 May 2005, 18:42
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