Let

where we assume |r| < 1. Multiplying on both sides by r gives

and subtracting this from
gives

As n → ∞, the exponential term will converge to 0, and the partial sums
will converge to

Now, we're given


We must have |r| < 1 since both sums converge, so


Solving for r by substitution, we have


Recalling the difference of squares identity, we have

We've already confirmed r ≠ 1, so we can simplify this to

It follows that

and so the sum we want is

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Well, their speeds are (

is Jack's speed, and

is Richard's.

They, together, can paint 12 houses in 35 days. To get a single house, we only have to calculate

which is very close to 3 (a bit below)
Answer:
The correct answer is actually B. x - 3y < 5
Step-by-step explanation:
Because you must convert the equation to y-intercept form first.
Which makes it y = 1/3x - 1.6
So y = 1.6 and using the slope of 1/3x you can find that x = 5