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Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

Re: Work-Rate Problem [#permalink]
31 Aug 2010, 07:26

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

formula is work = rate x time

for machine (X) k= r X 6 for machine (Y) k= r X 2 now take a value for k ( for ease which is a multiple of both mac X & y) take k=12 so rate of machine (x) is 2 so rate of machine (y) is 6

now work is 12k = 12x12 = 144 two machines working siman so rate = 6+2 =8 work = rate X time 144 = 8 X time so time = 18 so answer D