Question

A leaky valve on the water meter overcharges Ahmed for one Liter of water for every 2 months. The overcharged amount w varies directly with time t . (a) Find the equation that models the variation . (b) Solve the equation to find the number of months it will take for Ahmed to be overcharged for 10 liters of water leaked. Show all your steps

Answer 1

Answer:

20 months

Step-by-step explanation:

A leaky valve on the water meter overcharges Ahmed for one Liter of water for every $2$ months. The overcharged amount $w$ varies directly with time $t$.

(a)

As the overcharged amount $w$ varies directly with time $t$,

$w=kt$

Here, $k$ is a constant.

A leaky valve on the water meter overcharges Ahmed for one Liter of water for every $2$ months.

Put $w=1\,,\,t=2$

$1=2k\\k=\frac{1}{2}$

So,

$w=\frac{t}{2}$

(b)

To find the number of months it will take for Ahmed to be overcharged for 10 liters of water leaked, put $w=10$ in $w=\frac{t}{2}$

$10=\frac{t}{2}\\\\t=10(2)$

$t=20$ months