Question

A container is being filled with water at a steady rate. The graph shows how the volume of water in the container varies with the amount of time since the container began filling. We see that there are 4 gallons of water in the container when the container has been filling for 5 minutes. a. Define a formula to determines the volume (in gallons) of water in the container, v , in terms of the number of minutes, t, since the container began to fill.

Answer 1

Answer:  a. $v=\dfrac{2}{3}t$ and b. $t=\dfrac{3}{2}v$.

Step-by-step explanation:

Let as consider,

Volume (in gallons) of water in the container = v

The number of minutes = t

(a)

From the given graph it is clear that the line passing through the points (0,0) and (3,2). So, the equation of line is

$v-v_1=\dfrac{v_2-v_1}{t_2-t_1}(t-t_1)$

$v-0=\dfrac{2-0}{3-0}(t-0)$

$v=\dfrac{2}{3}t$

Therefore, the required formula is $v=\dfrac{2}{3}t$.

(b)

We have,

$v=\dfrac{2}{3}t$

Multiply both sides by 3/2.

$v\times \dfrac{3}{2}=\dfrac{2}{3}t\times \dfrac{3}{2}$

$\dfrac{3}{2}v=t$

$t=\dfrac{3}{2}v$

Therefore, the required formula is $t=\dfrac{3}{2}v$.