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?

Answer 1

HELP PLz

Answer 2

If it is direct variation, that means \[w = kt\] where \(k\) is a constant you need to determine. If \(t\) is in months, then we know that at \(t = 2.5\), \(w = 1\) because it takes 2.5 months to leak 1 gallon. Plug in those values and find \(k\). Then use the formula with the newly found value of \(k\) to find \(t\) when \(w = 8\).

Answer 3

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Answer 4

im lost

Answer 5

wow okay

Answer 6

\[w = kt\] is the form for direct variation of \(w\) with \(t\). You know that at \(t = 2.5, w = 1\). Plug in those values in \(w = kt\) and solve for the value of \(k\). \[1 = k(2.5)\]\[k = \]

Now put the value of \(k\) you found into the formula. We'll pretend that the value you found was 2 (hint: it isn't)
That would give us \[w = 2t\] as our formula, and to find the value of \(t\) when 8 gallons have leaked away, we solve \[8 = 2t\]

Answer 7

Thanks you man your a big help I got the answer I like the way you showed me instead of just giving me the answer thx man