A leaky valve on the water meter overcharges the residents for one gallon of water in every 2 1/2 months. The overcharged amount w varies directly with time t.

a. Find the equation that models this direct variation.
b. How many months it will take for the residents to be overcharged for 8 gallons of water?

Question

A leaky valve on the water meter overcharges the residents for one gallon of water in every 2 1/2 months. The overcharged amount w varies directly with time t.

a. Find the equation that models this direct variation. 
b. How many months it will take for the residents to be overcharged for 8 gallons of water?

anonymous · Answer

Direct variation gives us that w = kt.

'w' is the overcharge in gallons and 't' is the time in months.

So, t = 2.5, w = 1 (because it takes 2.5 months to leak 1 gallon). k is a constant that you need to find. 

1 = k (2.5); solving for 'k' gives you k = 0.4. 

Now you have the equation w = 0.4t and can plug in your 8 gallons for w and solve for the amount of time in months.