Company A and B

[gmatblood]

Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and the amount of time required to paint each home is the same, how many workers from Company B are required to 9 paint homes in 60 hours?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

[vaibhavgupta]

Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and the amount of time required to paint each home is the same, how many workers from Company B are required to 9 paint homes in 60 hours?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

IMOA

whts d OA?

[user123321]

company A:
8W - 7H - 84hr
=>1W - 1H - (84/7)*8 = 96 hrs

company A+B's work:
3Wa+5Wb - 9H - 96 hrs
3Wa+5Wb - 1H - 96/9 = 32/3
5Wb's fraction of work = (3/32)-3/96 = 1/16 => 5Wb take 16 hrs to construct 1H
so 5Wb - 1H - 16 hrs

company B:
Wx - 9H - 60 hrs
Wx - 1H - 60/9 = 20/3
but we know
5Wb - 1H - 16 hrs
combining
Wx*20/3 = 16*5
solving for Wx we get 12 hrs

nice problem in work and time

user123321