Answer
The 180 gal/h pump was operated for 2.5 hours. The 250 gal/h pump was operated for 3.5 hours.
Work Step by Step
Let x be the time in operation of the 180 gal/h pump and y be the time in operation of the 250 gal/h pump.
$x+y=6$ since the total test time was 6 hours.
$180x+250y=1325$ since the total amount pumped was 1325 gal.
Multiply both sides of the first equation by -250, then add the two equations.
$-250x-250y=-1500$
$\underline{\ \ \ 180x+250y=\ \ \ 1325}$
$\ -70x\ \ \ \ \ \ \ \ \ \ \ \ =-175$ $\longrightarrow$ divide both sides by -70 to solve for x
$-70x\div-70=-175\div-70$
$x=2.5$
Substitute 2.5 for x in the first equation to solve for y.
$2.5+y=6$
$2.5+y-2.5=6-2.5$
$y=3.5$
