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

20 months

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=(1)/(2)`

So,

`w=(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=(t)/(2)`

`10=(t)/(2)\\\\t=10(2)\\`

`t=20` months