A leaky valve on the water meter overcharges the residents for one gallon of water every 1 1 over 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?

w = 3 over 4t; 62 over 3 months
w = 4 over 3t; 62 over 3 months
w = 3 over 4t; 33 over 4 months
w = 4 over 3t; 33 over 4 months

Question

A leaky valve on the water meter overcharges the residents for one gallon of water every 1 1 over 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?

w = 3 over 4t; 62 over 3 months
w = 4 over 3t; 62 over 3 months
w = 3 over 4t; 33 over 4 months
w = 4 over 3t; 33 over 4 months

ganeshie8 · Answer

it overcharges $1$ gallon for every $\large  1 \frac{1}{3} $ months

anonymous · Answer

oh ok...so then it'd be the last one?

ganeshie8 · Answer

ive second thoughts, scratch that

anonymous · Answer

Ok..

ganeshie8 · Answer

$\large 1 \frac{1}{3}= \frac{4}{3}  $


if w is the gallons over charged, every 4/3 months u will be overcharged 1 gallone

so, the required equation wud be

$\large \color{red}{w= \frac{3}{4}t} $

where,

$w$ is gallons over charged

$t$ is time in months

ganeshie8 · Answer

this will work, cus, when u put in t = 4/3 months, u wud get 1 gallon

anonymous · Answer

Oh ok, I see now.

ganeshie8 · Answer

good :) next do the second part
simply replace w by 5 and solve that equation for t

ganeshie8 · Answer

$\large \color{red}{w= \frac{3}{4}t} $

u wanto knw how many months(t) it will take for residents to be overcharged
 5 gallons

 so, put w = 5


$\large \color{red}{5= \frac{3}{4}t} $


solve  $t$

anonymous · Answer

wouldn't I, multiply or something on those lines the 5 and the fraction?

ganeshie8 · Answer

multiply 4 both sides

ganeshie8 · Answer

$\large \color{red}{5= \frac{3}{4}t} $
multiply 4 both sides

$\large \color{red}{5 \times 4= 4 \times \frac{3}{4}t} $

$\large \color{red}{20 = 3t} $

ganeshie8 · Answer

next divide 3 both sides

ganeshie8 · Answer

u wud get

$\large \frac{20}{3}  = t $

anonymous · Answer

then woldnt I get 6

ganeshie8 · Answer

u can convert it to mixed fraction like below :-

$\large \frac{20}{3} = \frac{18+2}{3} = 6 + \frac{2}{3} = 6 \frac{2}{3}$

anonymous · Answer

how did you get the 18+2?

ganeshie8 · Answer

see if that makes more/less sense... 

to be clear,  the answer is first option.

ganeshie8 · Answer

20 = 18+2

anonymous · Answer

oh durr.. lol

ganeshie8 · Answer

i believe u asked me why i wrote 20 as 18+2, but not 17+3, or 16+4

right ?

anonymous · Answer

yes

ganeshie8 · Answer

its just that i figured out 18 is the multiple of 3, so it cancels... 
once u knw how to convert  to mixed fractions, u will see ...