The Hall family and the Nguyen family each used their sprinklers last summer. The water output rate for the Hall family's sprinkler was 35L per hour. The water output rate for the Nguyen family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1050L. How long was each sprinkler used?

Nguyen family uses sprinkler for 35 hours while the Hall family uses sprinkler for 15 hours

Step-by-step explanation:

Let h and n be the number of hours that the Hall and Nguyen family individually use their sprinkler for, respectively. Since they use for a combined total of 50 hours, h + n = 50, or h = 50 - n

Also their total water output is 1050 L, we can have the following equation

35h + 15n = 1050

Substitute h = 50 - n and we have

35 (50 - n) + 15n = 1050

1750 - 35n + 15n = 1050

35n - 15n = 1750 - 1050

20n = 700

n = 35 hours

h = 50 - n = 50 - 35 = 15 hours