Question

A total of 110 gallons of water can follow through Hose B in minutes. Which hose has a faster water ow rate, in gallons per minute, and what is that rate?

Answer 1

Hose B

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
`(x_1,y_1)\ and\ (x_2,y_2)` is given by:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)`

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:

`y-0=(12-0)/(2-0)(x-0) \\\\y=6x`

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