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A completes the given task in 12 hours. B completes the

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A completes the given task in 12 hours. B completes the [#permalink] New post 02 Nov 2007, 12:32
A completes the given task in 12 hours.
B completes the given task in 9 hours.

A does the work for 1/3 of the work working at a conistant rate. Then B joins him for the rest of the work. How many hours did it take A to complete the task?
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 [#permalink] New post 02 Nov 2007, 12:41
At first it takes A 4 hours to do 1/3 of the work (1/3 of the total time). Next you combine A's rate (1/12 of the job per hour) and B's rate (1/9)
(1/12)+(1/9)=(7/36) Now you use t=d/r to calculate the time for 2/3 of the job at a rate of 7/36. (2/3)/(7/36) = (2/3)(36/7) = 24/7 = 3 and 3/7

4+3 and 3/7 = 7 and 3/7
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 [#permalink] New post 02 Nov 2007, 12:49
maybeitssteve is correct !

A - 1/12 ---> in one hour
B - 1/9 ---> in one hour

A+B - 21/108 = 7/36 ---> in one hour

A alone 12/3 = 4 hours --> one third of the work

A+B ---> two third of the work ---> 72/21 = 24/7

4+24/7 = (28+24)/7 = 52/7 houres

:)
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 [#permalink] New post 04 Nov 2007, 17:53
KillerSquirrel wrote:
maybeitssteve is correct !

A - 1/12 ---> in one hour
B - 1/9 ---> in one hour

A+B - 21/108 = 7/36 ---> in one hour

A alone 12/3 = 4 hours --> one third of the work

A+B ---> two third of the work ---> 72/21 = 24/7

4+24/7 = (28+24)/7 = 52/7 houres

:)


Nice!

I also made up this question from one of the Challenges

A = 1/12 of the work done in an hour
B = 1/9

Working together 1/ (1/9) + (1/12)

(1/9) + (1/12) = 4/36 + 3/26 = 7/36
1/(7/36) = 36/7

1/3 of the work of A
1/3(12) = 4

A's time is 4 + 2/3(together rate)
4 + 2/3(36/7)
4 + (72/21)
4 + 24/7
4 + 3 and 3/7
7 hours and 3/7th of an hour

3/7 of 60 minutes
approx 26 minutes

7 hours 26 minutes
  [#permalink] 04 Nov 2007, 17:53
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