Question

The Lopez family and the Russell family each used their sprinklers last summer. The water output rate for the Lopez family's sprinkler was 15 L per hour. The water output rate for the Russell family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1050 L . How long was each sprinkler used?

Answer 1

L = hours used by the Lopez's sprinkler

R = hours used by the Russell's sprinkler

so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.

likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.

we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.

we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.

$\bf \begin{cases} L+R=45\implies \boxed{L}=45-R\\ 15L+40R=1050\\ ----------\\ 15\left(\boxed{45-R} \right)+40R=1050 \end{cases} \\\\\\ 675-15R+40R=1050\implies 25R=375\implies R=\cfrac{375}{25}\\\\\\ R=15$

how long was the Lopez's on for?  well, L = 45 - R.