# Water is leaking from a tank. The volume of water in the tank after 1 hour is 100L and after 5hours the volume is 20L. Assuming the relationship is linear, find a rule and then state the initial...

Water is leaking from a tank. The volume of water in the tank after 1 hour is 100L and after 5hours the volume is 20L. Assuming the relationship is linear, find a rule and then state the initial volume of water in the tank.

lemjay | Certified Educator

To solve , let V be the volume of water in the tank. And, let t be number of hours that the water was leaking.

So the given values of t and V are:
t        V
1        100
5        20

If we express them as order pairs, it would be (1,100) and (5,20).

Now that we have our two points, determine the slope of the line connecting them. So, apply the formula:

`m=(y_2-y_1)/(x_2-x_1)`

For our problem, it will be:

`m=(V_2-V_1)/(t_2-t_1) `

`m=(20-100)/(5-1)=(-80)/4=-20`

Hence, the slope of the line is -20.

Then, use the point-slope form to get the equation.

`y - y_1 =m(x - x_1)`

For our problem, it will be:

`V-V_1=m(t - t_1)`

`V-100=-20(t-1)`

`V-100=-20t+20`

Then, isolate the V.

`V=-20t+20+100`

`V=-20t+120`

Therefore, the volume of water that remains inside the tank when the water was leaking for t hours can be determined using the equation

`V=-20t +120` .

To solve for the initial amount of water in the tank, plug-in t=0 to the equation.

`V=-20(0)+120 = 0+120=120`

Thus, the initial volume of water in the tank is 120L.