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 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 24k bottles? Choices:
A) 48
B) 42
C) 45
D) 98
E) 96
x rate = k/6   y rate = k/12   k/6 + k/12 = 24k / T   solving T = 96   Answer 96
<result>E</result>
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 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 24k bottles?