Question

the gonzales family and the murphy family each used their sprinklers last summer. the water output rate for the gonzales familys sprinkler was 35 l per hour. the water output rate for the murphy familys sprinkler was 15 l per hour. the families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1775 l.
how long was each sprinkler used?
gonzales family: $square$ hours
murphy familys sprinkler: $square$ hours

Explanation:

Step1: Define variables for time

Let $x$ = Gonzales sprinkler time (hours), $y$ = Murphy sprinkler time (hours).

Step2: Set up total time equation

Total combined time is 65 hours:
$x + y = 65$

Step3: Set up total water equation

Total water is sum of each family's usage:
$35x + 15y = 1775$

Step4: Solve time equation for $y$

Rearrange to isolate $y$:
$y = 65 - x$

Step5: Substitute $y$ into water equation

Substitute and simplify:
$35x + 15(65 - x) = 1775$
$35x + 975 - 15x = 1775$
$20x + 975 = 1775$

Step6: Solve for $x$

Isolate $x$ and calculate:
$20x = 1775 - 975$
$20x = 800$
$x = \frac{800}{20} = 40$

Step7: Calculate $y$

Use $y = 65 - x$:
$y = 65 - 40 = 25$

Answer:

Gonzales family's sprinkler: 40 hours
Murphy family's sprinkler: 25 hours