Answer:
Hose B
Step-by-step explanation:
Charles needs to fill a large fish tank with water using a hose. he has two hoses from which to choose. Water flows through each hose at a constant rate. The graph below shows the amount of water, in gallons , that flows through holes A based on the number of minutes used. A total of 110 gallons of water can flow through Hose B in 10 minutes. Which hose has a faster water rate, in gallons per minute, and what is that rate?
Solution:
The equation of a linear function is:
y = mx + b
where m is the rate of change and b is the initial value of y.
The equation of a line passing through two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Let y represent the amount of water in gallons and let x represent the time in minutes.
For hose A, we can see that the graph passes through the point (0, 0) and (2, 12). Hence:
[tex]y-0=\frac{12-0}{2-0}(x-0) \\\\y=6x[/tex]
Therefore hose A has a flow rate of 6 gallons per minute.
110 gallons of water flow through hose B in 10 minutes. Therefore:
Flow rate of hose B = 110 gallons / 10 minutes = 11 gallons per minute
Therefore hose B has a higher flow rate
