Question

The Bailey family and the Howard family each used their sprinklers last summer. The water output rate for the Bailey family's sprinkler was 35 L per hour. The water output rate for the Howard family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 70 hours, resulting in a total water output of 1850 L. How long was each sprinkler used?

a. Bailey family used the sprinkler for 40 hours, and Howard family used it for 30 hours.
b. Bailey family used the sprinkler for 50 hours, and Howard family used it for 20 hours.
c. Bailey family used the sprinkler for 25 hours, and Howard family used it for 45 hours.
d. Bailey family used the sprinkler for 35 hours, and Howard family used it for 35 hours.

Answer 1

The Bailey family used the sprinkler for 40 hours and the Howard family used it for 30 hours.

Step-by-step explanation:

To find how long each sprinkler was used, we can set up a system of equations. Let x represent the number of hours the Bailey family used their sprinkler and y represent the number of hours the Howard family used their sprinkler. We can then create the following equations:

35x + 15y = 1850 (the total water output)

x + y = 70 (the combined total number of hours)

Now we can solve this system of equations using any method we prefer. One way is to multiply the second equation by 15 to make the coefficients of y in both equations the same:

35x + 15y = 1850

15x + 15y = 1050

Subtract the second equation from the first equation:

(35x + 15y) - (15x + 15y) = 1850 - 1050

This simplifies to:

20x = 800

Divide both sides by 20:

x = 40

Substitute the value of x back into the second equation:

40 + y = 70

Subtract 40 from both sides:

y = 30

So, the Bailey family used the sprinkler for 40 hours and the Howard family used it for 30 hours. Therefore, the correct option is a. Bailey family used the sprinkler for 40 hours, and Howard family used it for 30 hours.