Question

- Hose A fills a water truck at the constant rate of 60 gallons every 15 minutes. Hose B fills a water truck at a constant rate that

is represented by the function y = 3x, where y is the total number of aallons filled in x minutes. Which BEST compares the rates of
the two hoses?
The rate of Hose A is 3 gallons per minute more than the rate of Hose B.
The rate of Hose B is 3 gallons per minute more than the rate of Hose A.
The rate of Hose A is 1 gallon per minute more than the rate of Hose B.
D)
The rate per minute is the same for Hose A and Hose B.

Answer 1

Answer: The correct option is

(C) The rate of Hose A is 1 gallon per minute more than the rate of Hose B.

Step-by-step explanation: Given that Hose A fills a water truck at the constant rate of 60 gallons every 15 minutes.

Hose B fills a water truck at a constant rate that is represented by the function y = 3x, where y is the total number of gallons filled in x minutes.

We are to select the statement that best compares the rates of the two horses.

For Hose A :

In every 15 minutes, number of gallons filled = 60.

So, in every 1 minute, number of gallons filled is given by

`(60)/(15)=4.`

That is, Hose A is filled at the rate of 4 gallons per minute.

For Hose B :

The given function is y = 3x, where y is the total number of gallons filled in x minutes.

So, in 1 minute, number of gallons filled = 3 × 1 = 3.

That is, Hose B is filled at the rate of 3 gallons per minute.

Therefore, we get

`\textup{number of gallons filled per minute for Hose A}-\textup{number of gallons filled per minute for Hose B}\\\\=4-3\\\\=1~\textup{gallon per minute}.`

Thus, the rate of Hose A is 1 gallon per minute more than the rate of Hose B.

Option (C) is CORRECT.

Answer 2

"The rate of Hose A is 1 gallon per minute more than the rate of Hose B"

Explanation:

Hose A:

60 gallons every 15 minutes means

60/15 = 4 gallons per minute

Hose B:

y = 3x

y is gallons

x is minutes

we put x = 1 and get:

y = 3*1 = 3

That means 3 gallons per minute

Thus,

the correct choice is C), or third option. 4 is 1 greater than 3 so Hose A is 1 gallons per minute more than the rate of Hose B.