A leaky value on the water meter overcharge the residents for one gallon of water every 1 1/3 months.the overcharged amount w varies directly with time t find the equation that models this direct variation how many months it will take for the residents to be overcharged for 5 gallons of water?answers are w=3/4t;6 2/3month, w=4/3t;6 2/3 month., w=3/4;3 3/4month, w=4/3;3 3/4month thanks

jkl

To find the equation that models the direct variation between the overcharged amount (w) and time (t), we are given that the overcharged amount of water (w) varies directly with time (t), with an overcharge of 1 gallon every 1 1/3 months.

First, we need to determine the constant of variation, which is the rate at which the overcharged amount increases with time. In this case, it is 1 gallon every 1 1/3 months. We can write this constant as 4/3.

So, the equation that models the direct variation can be written as:

w = (4/3)t

Now, to calculate how many months it will take for the residents to be overcharged for 5 gallons of water, we need to substitute the value of w (5 gallons) into the equation and solve for t:

5 = (4/3)t

To solve for t, we can multiply both sides of the equation by 3/4:

(3/4) * 5 = (3/4) * (4/3)t

15/4 = t

So, it will take the residents 15/4 months to be overcharged for 5 gallons of water, which can also be simplified to 3 3/4 months.

Therefore, the correct answer is w = (4/3)t; 3 3/4 months.