The Gray family and the Wright family each used their sprinklers last summer. The Gray family's sprinkler was used for 25 hours. The Wright family's sprinkler was used for 15 hours. There was a combined total output of $850 \mathrm{~L}$ of water. What was the water output rate for each sprinkler if the sum of the two rates was $40 \mathrm{~L}$ per hour?

Step 1 ：Let's denote the water output rate of the Gray family's sprinkler as G and the water output rate of the Wright family's sprinkler as W.

Step 2 ：We have two equations based on the problem: \(G + W = 40\) (the sum of the two rates was 40 L per hour) and \(25G + 15W = 850\) (the combined total output of water).

Step 3 ：We can solve this system of equations to find the values of G and W.

Step 4 ：The solution to the system of equations is {G: 25, W: 15}.

Step 5 ：Final Answer: The water output rate for the Gray family's sprinkler was \(\boxed{25 \mathrm{~L/hour}}\) and for the Wright family's sprinkler was \(\boxed{15 \mathrm{~L/hour}}\).