Question #112a0

1 Answer
Mar 7, 2017

Answer:

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

Explanation:

Let
#color(white)("XXX")L# be the number of hours the Lopez sprinkler was used, and
#color(white)("XXX")F# be the number of hours the Flores sprinkler was used.

We are told:
[1]#color(white)("XXX")40L+25F=1100#
[2]#color(white)("XXX")L+F=35color(white)("XX")rarrcolor(white)("XX")L=35-F#

[2] implies that
[3]#color(white)("XXX")40L=1400-40F#

Combining [3] with [1], we have
[4]#color(white)("XXX")1400-40F+25F=1100#

Simplifying
[5]#color(white)("XXX")-15F=-300#
or
[6]#color(white)("XXX")F=30#

If #F=20# and #L=35-F#
#color(white)("XXX")L=15#