Answer:
7.5 minutes
Step-by-step explanation:
Given
See attachment for complete question
Let
[tex]t \to time[/tex]
[tex]y \to capacity[/tex]
From the question, we have the following points
[tex](t_1,y_1) = (0,7)[/tex] --- When he first sees it
[tex](t_2,y_2) = (3,5)[/tex] --- 3 minutes later
First, we calculate the rate (m)
[tex]m = \frac{y_2 -y_1}{t_2 -t_1}[/tex]
[tex]m = \frac{5 -7}{3 -0}[/tex]
[tex]m = -\frac{2}{3}[/tex]
The discharge rate is 2/3 gallons per minute
To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons
To calculate time (t), we have:
[tex]Rate * Time = Capacity[/tex]
[tex]\frac{2}{3} * t = 5[/tex]
Solve for t
[tex]t = 5 *\frac{3}{2}[/tex]
[tex]t = \frac{15}{2}[/tex]
[tex]t = 7.5[/tex]
