The Sanchez family and the Price family each used their sprinklers last summer. The water output rate for the Sanchez family's sprinkler was 30 L per hour. The water output rate for the Price family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 1275 L. How long was each sprinkler used?
Let's start by setting up some variables:
- Let's call the number of hours the Sanchez family used their sprinkler "x"
- Let's call the number of hours the Price family used their sprinkler "y"
We know that the water output for the Sanchez family's sprinkler is 30 L/hour, so the total amount of water they used is 30x. Similarly, the total amount of water used by the Price family is 15y.
We also know that the families used their sprinklers for a combined total of 60 hours, so x + y = 60.
Finally, we know that the total water output for both families was 1275 L, so 30x + 15y = 1275.
We can use these two equations to solve for x and y. First, let's simplify the second equation by factoring out a 15:
15(2x + y) = 1275
Divide both sides by 15:
2x + y = 85
Now we have two equations and two variables. We can solve for one of the variables in terms of the other, and then substitute that into the other equation to solve for the remaining variable. Let's solve for y in terms of x from the first equation:
y = 60 - x
Now we can substitute that into the second equation:
2x + (60 - x) = 85
Simplify and solve for x:
x = 25
So the Sanchez family used their sprinkler for 25 hours. We can use the first equation to find y:
30x + 15y = 1275
30(25) + 15y = 1275
750 + 15y = 1275
15y = 525
y = 35
So the Price family used their sprinkler for 35 hours.
To check our work, we can make sure that the total water output adds up to 1275:
30x + 15y = 1275
30(25) + 15(35) = 750 + 525 = 1275
It does, so we have our solution: the Sanchez family used their sprinkler for 25 hours and the Price family used their sprinkler for 35 hours.