20 bottles filled in 1 minute gives you a unit rate of
[tex] \dfrac{20~bottles}{minute} [/tex]
Now let's look at the choices.
Option A.
[tex] \dfrac{1~bottle}{20~sec} [/tex]
There are 60 seconds in a minute, so there are 3 20-second periods in a minute.
[tex] \dfrac{1~bottle}{20~sec} = \dfrac{3 \times 1~bottle}{3 \times 20~sec} = \dfrac{3~bottles}{minute} [/tex]
Option A. is not it.
Option B.
[tex] \dfrac{3000~bottles}{15~minutes} = \dfrac{3000/15 bottles}{15/15 minutes} = \dfrac{200~bottles}{ minute} [/tex]
Option B. is not it.
Option C.
[tex] \dfrac{10~bottles}{50~sec} = \dfrac{10/50 * 60~bottles}{50/50 * 60~sec} = \dfrac{12~bottles}{1~minute} [/tex]
Option C is not it.
Option D.
[tex] \dfrac{50~bottles}{2.5~minutes} = \dfrac{50 \div 2.5 ~bottles}{2.5 \div 2.5~minute} = \dfrac{20~bottles}{minute} [/tex]
Option D. is the correct answer.
