Question

The Turner family and the James family each used their sprinklers last summer. The water output rate for the Turner family's sprinkler was

25L
per hour. The water output rate for the James family's sprinkler was
15L
per hour. The families used their sprinklers for a combined total of
75
hours, resulting in a total water output of
1475K
. How long was each sprinkler used?

Answer 1

x will be the turner family, y will be the James family
using the givens we construct first this equation

`25x + 15y = 1475`
then this one


`x + y = 75`
multiply the second by 15 to get


`15x + 15y = 1125`
now subtract it from the first to get


`10x = 350 \\ x = 35`
substitute to find that


`35 + y = 75 \\ y = 40`
35 hours for Turner, 40 hours for James