Question

ASAP: 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. Which BEST compares the rates of the two hoses?

A) The rate of Hose A is 3 gallons per minute more than the rate of Hose B.


B) The rate of Hose B is 3 gallons per minute more than the rate of Hose A.


C) 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

The correct answer is option C,

Explanation:

Hose-A fills 60 gallons of water in 15 minutes .

Rate of Hose-A at which it fills water truck =
`R_a=(60 gal)/(15 min)=4 gal/min`

Hose-B fills water truck , its function is given as:

y = 3x

Where y is the total number of gallons filled in x minutes.

Rate of Hose-B at which it fills water truck =
`R_b=(y gal)/(xmin)=(3x)/(x) gal/min=3 gal/min`

Difference in rates of both hoses:

`R_a-R_b=4 gal/min - 4gal/min = 1 gal/min`

`R_a-R_b=1 gal/min`

`R_a=R_b+1 gal/min`

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

Answer 2

C

Explanation:

Hose A:

60 gallons every 15 minutes mean:

60 / 15 = 4 gallons per minute

For Hose B:

If we put x = 1, we can find gallons (y) per minute (x)

y = 3 x

y = 3(1)

y = 3

That means 3 gallons per minute

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