He kelly family and the stewart family each used their sprinklers last summer. the water output rate for the kelly family's sprinkler was 20l per hour. the water output rate for the stewart family's sprinkler was 40l per hour. the families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 2100l . how long was each sprinkler used?

This problem is actually under the subject of Mathematics, particularly, Algebra. For work problems, you can use a convenient technique of dimensional analysis. This is done by multiplying units of measurement, then cancelling out like terms in order to come up with the units of the final answer. For this problem, the total amount of liters is 2,100. So, the equation would be

Volume of Kelly's family + Volume of Stewart's family = 2,100

However, we are only given the rates for each family in liters per hour. To come up with the final answer with a unit of measurement in Liters, we must multiple the rate of L/hour with the individual time. Let x be the time Kelly's sprinkler was used, and y for Stewart's family.

(20 L/h)(x hours) + (40 L/h)(y hours) = 2,100

This is the first equation. The second equation is the total time. 

x + y = 65 hours

Rearranging the equation, y = 65 - x. Let's substitute this to the first equation.

20x + 40(65-x) = 2,100

Solving for x, then substituting it to the second equation to obtain y,

x = 25 hours
25 + y = 65
y = 40 hours.

Thus, Kelly's sprinkler was used for 25 hours, while Stewart's sprinkler was used for 40 hours.