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

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CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 349 [0], given: 4

A completes the given task in 12 hours. B completes the [#permalink]  02 Nov 2007, 11:32
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?
Intern
Joined: 21 Jun 2007
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 0

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
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [0], given: 0

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

CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 349 [0], given: 4

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 + 3 and 3/7
7 hours and 3/7th of an hour

3/7 of 60 minutes
approx 26 minutes

7 hours 26 minutes
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