# Question #112a0

Mar 7, 2017

The Lopez sprinkler was used for $15$ hours.
The Flores sprinkler was used for $20$ hours.

#### Explanation:

Let
$\textcolor{w h i t e}{\text{XXX}} L$ be the number of hours the Lopez sprinkler was used, and
$\textcolor{w h i t e}{\text{XXX}} F$ be the number of hours the Flores sprinkler was used.

We are told:
[1]$\textcolor{w h i t e}{\text{XXX}} 40 L + 25 F = 1100$
[2]$\textcolor{w h i t e}{\text{XXX")L+F=35color(white)("XX")rarrcolor(white)("XX}} L = 35 - F$

[2] implies that
[3]$\textcolor{w h i t e}{\text{XXX}} 40 L = 1400 - 40 F$

Combining [3] with [1], we have
[4]$\textcolor{w h i t e}{\text{XXX}} 1400 - 40 F + 25 F = 1100$

Simplifying
[5]$\textcolor{w h i t e}{\text{XXX}} - 15 F = - 300$
or
[6]$\textcolor{w h i t e}{\text{XXX}} F = 30$

If $F = 20$ and $L = 35 - F$
$\textcolor{w h i t e}{\text{XXX}} L = 15$