the water hose fills a bucket at 1/3 gallon per minute. How many minutes does it take to fill up 2-gallon bucket

6 minutes

Work Shown

1/3 gallon : 1 minute

3*(1/3 gallon) : 3*(1 minute)

1 gallon : 3 minutes

2*(1 gallon) : 2*(3 minutes)

2 gallons : 6 minutes

Explanations:

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb